diff --git a/test/freeflow/navierstokes/navierstokestestproblem.hh b/test/freeflow/navierstokes/navierstokestestproblem.hh
index afe4ef91d06cd15185355d80111a591b17cf91b4..ab468207239f3265279ea65f8d71aaeb756c8dab 100644
--- a/test/freeflow/navierstokes/navierstokestestproblem.hh
+++ b/test/freeflow/navierstokes/navierstokestestproblem.hh
@@ -111,9 +111,7 @@ namespace Dumux
   public:
       NavierStokesTestProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-      {
-        eps_ = 1e-6;
-      }
+      {}
 
       /**
        * \name Problem parameters
@@ -280,7 +278,7 @@ namespace Dumux
         return globalPos[1] > this->bBoxMax()[1] - eps_;
       }
 
-      Scalar eps_;
+      static constexpr Scalar eps_ = 1e-6;
   };
 } //end namespace
 
diff --git a/test/freeflow/stokes/stokestestproblem.hh b/test/freeflow/stokes/stokestestproblem.hh
index 6a36015c2e0d041dc6e4b875925b0014220fc650..dc79c2ec8abcc381c4ae449abd6d477e6e3dff98 100644
--- a/test/freeflow/stokes/stokestestproblem.hh
+++ b/test/freeflow/stokes/stokestestproblem.hh
@@ -112,9 +112,7 @@ class StokesTestProblem : public StokesProblem<TypeTag>
 public:
     StokesTestProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-    {
-        eps_ = 1e-6;
-    }
+    {}
 
     /*!
      * \name Problem parameters
@@ -260,7 +258,7 @@ private:
     bool onUpperBoundary_(const GlobalPosition &globalPos) const
     { return globalPos[1] > this->bBoxMax()[1] - eps_; }
 
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
 };
 
 } //end namespace
diff --git a/test/freeflow/stokes2c/stokes2ctestproblem.hh b/test/freeflow/stokes2c/stokes2ctestproblem.hh
index 81a61c6fcb62fca4cf715113b5c263383be38ec7..5c824d889172e3a88c6d261db63ebd5c95013ebc 100644
--- a/test/freeflow/stokes2c/stokes2ctestproblem.hh
+++ b/test/freeflow/stokes2c/stokes2ctestproblem.hh
@@ -110,8 +110,6 @@ public:
     Stokes2cTestProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
     {
-        eps_ = 1e-6;
-
         // initialize the tables of the fluid system
         FluidSystem::init();
     }
@@ -248,7 +246,7 @@ private:
     bool onUpperBoundary_(const GlobalPosition &globalPos) const
     { return globalPos[1] > this->bBoxMax()[1] - eps_; }
 
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
 };
 } //end namespace
 
diff --git a/test/freeflow/stokes2cni/stokes2cnitestproblem.hh b/test/freeflow/stokes2cni/stokes2cnitestproblem.hh
index 1e6fe9953485f271edf2a09929107ff0ea41ce98..ee811947d49d0d87491abf20f8e2b4b4fef81d25 100644
--- a/test/freeflow/stokes2cni/stokes2cnitestproblem.hh
+++ b/test/freeflow/stokes2cni/stokes2cnitestproblem.hh
@@ -130,8 +130,6 @@ public:
     Stokes2cniTestProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
     {
-        eps_ = 1e-6;
-
         // initialize the tables of the fluid system
         FluidSystem::init();
 
@@ -236,8 +234,8 @@ private:
         values[pressureIdx] = 1e5 + 1.189*this->gravity()[1]*globalPos[1];
         values[massOrMoleFracIdx] = 1e-4;
         values[temperatureIdx] = 283.15;
-        if(globalPos[0] < 0.75 && globalPos[0] > 0.25 &&
-                globalPos[1] < 0.75 && globalPos[1] > 0.25)
+        if(globalPos[0] < 0.75 + eps_ && globalPos[0] > 0.25 - eps_ &&
+                globalPos[1] < 0.75 + eps_ && globalPos[1] > 0.25 - eps_)
         {
             values[massOrMoleFracIdx] = 0.9e-4;
             values[temperatureIdx] = 284.15;
@@ -274,7 +272,7 @@ private:
                 || onLowerBoundary_(globalPos) || onUpperBoundary_(globalPos));
     }
 
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     Scalar velocity_;
 };
 } //end namespace
diff --git a/test/freeflow/zeroeq/zeroeqchanneltestproblem.hh b/test/freeflow/zeroeq/zeroeqchanneltestproblem.hh
index d6c568b4f3d0644257a1699afe7961989b7a6630..f98c73d3dc7abd8429d7279dc5ad5f156b4dd067 100644
--- a/test/freeflow/zeroeq/zeroeqchanneltestproblem.hh
+++ b/test/freeflow/zeroeq/zeroeqchanneltestproblem.hh
@@ -114,8 +114,6 @@ public:
     ZeroEqChannelTestProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
     {
-        eps_ = 1e-6;
-
         injectionVelocity_ = GET_RUNTIME_PARAM(TypeTag, Scalar, Problem.InjectionVelocity);
     }
 
@@ -254,7 +252,7 @@ private:
     bool onUpperBoundary_(const GlobalPosition &globalPos) const
     { return globalPos[1] > this->bBoxMax()[1] - eps_; }
 
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     Scalar injectionVelocity_;
 };
 
diff --git a/test/freeflow/zeroeq/zeroeqtestproblem.hh b/test/freeflow/zeroeq/zeroeqtestproblem.hh
index 137ee962d7498bc72fc0b140d9662ccb2a84dba8..78b2af8c91734a21456503fa23cde5a5dc20e4dd 100644
--- a/test/freeflow/zeroeq/zeroeqtestproblem.hh
+++ b/test/freeflow/zeroeq/zeroeqtestproblem.hh
@@ -116,8 +116,6 @@ public:
     ZeroEqTestProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
     {
-        eps_ = 1e-6;
-
         injectionVelocity_ = GET_RUNTIME_PARAM(TypeTag, Scalar, Problem.InjectionVelocity);
     }
 
@@ -240,7 +238,7 @@ private:
     bool onUpperBoundary_(const GlobalPosition &globalPos) const
     { return globalPos[1] > this->bBoxMax()[1] - eps_; }
 
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     Scalar injectionVelocity_;
 };
 
diff --git a/test/freeflow/zeroeq2c/zeroeq2ctestproblem.hh b/test/freeflow/zeroeq2c/zeroeq2ctestproblem.hh
index b0b0b38b571a15a039c78b70883123f1745d257e..fd891357454f6c46c0de2bc121950f3c41088802 100644
--- a/test/freeflow/zeroeq2c/zeroeq2ctestproblem.hh
+++ b/test/freeflow/zeroeq2c/zeroeq2ctestproblem.hh
@@ -222,7 +222,7 @@ private:
             values[velocityXIdx] = injectionVelocity_;
 
         Scalar middle = 0.5 * (this->bBoxMax()[1] - this->bBoxMin()[1]);
-        if (onLeftBoundary_(globalPos) && globalPos[1] > middle - 0.2 && globalPos[1] < middle + 0.2)
+        if (onLeftBoundary_(globalPos) && globalPos[1] > middle - 0.2 - eps_ && globalPos[1] < middle + 0.2 + eps_)
             values[massOrMoleFracIdx] = injectionConcentration_;
 
         values[pressureIdx] = 1e5;
diff --git a/test/freeflow/zeroeq2cni/zeroeq2cnitestproblem.hh b/test/freeflow/zeroeq2cni/zeroeq2cnitestproblem.hh
index a3b1f19fc2ae6c1be9fbf4a45c24040af32f8fcf..e1f5ce4dcd080811ba8b6fe9dda36dadb2a593bb 100644
--- a/test/freeflow/zeroeq2cni/zeroeq2cnitestproblem.hh
+++ b/test/freeflow/zeroeq2cni/zeroeq2cnitestproblem.hh
@@ -115,8 +115,6 @@ public:
         , flowNormal_(GET_PARAM_FROM_GROUP(TypeTag, int, ZeroEq, FlowNormal))
         , wallNormal_(GET_PARAM_FROM_GROUP(TypeTag, int, ZeroEq, WallNormal))
     {
-        eps_ = 1e-6;
-
         injectionVelocity_ = GET_RUNTIME_PARAM(TypeTag, Scalar, Problem.InjectionVelocity);
         injectionConcentration_ = GET_RUNTIME_PARAM(TypeTag, Scalar, Problem.InjectionConcentration);
         wallTemperature_ = GET_RUNTIME_PARAM(TypeTag, Scalar, Problem.WallTemperature);
@@ -244,7 +242,7 @@ private:
 
     const unsigned int flowNormal_;
     const unsigned int wallNormal_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     Scalar injectionVelocity_;
     Scalar injectionConcentration_;
     Scalar wallTemperature_;
diff --git a/test/geomechanics/el1p2c/el1p2cproblem.hh b/test/geomechanics/el1p2c/el1p2cproblem.hh
index 741662f4f574638d301def3040d13e2351686e1e..592bda3fa9fa217850b1046645c8b9104a8b5da1 100644
--- a/test/geomechanics/el1p2c/el1p2cproblem.hh
+++ b/test/geomechanics/el1p2c/el1p2cproblem.hh
@@ -204,9 +204,9 @@ class El1P2CProblem: public ImplicitPorousMediaProblem<TypeTag>
     {
         values = Scalar(0.0);
 
-            if(globalPos[0] < 6 && globalPos[0] > 4
-                    && globalPos[1] < 6 && globalPos[1] > 4
-                    && globalPos[2] < 6 && globalPos[2] > 4)
+            if(globalPos[0] < 6 + eps_ && globalPos[0] > 4 - eps_
+                    && globalPos[1] < 6 + eps_ && globalPos[1] > 4 - eps_
+                    && globalPos[2] < 6 + eps_ && globalPos[2] > 4 - eps_)
             {
                 values[0] = 1.e-3;
                 values[1] = 1.e-4;
diff --git a/test/geomechanics/el2p/el2pproblem.hh b/test/geomechanics/el2p/el2pproblem.hh
index 65cf9bb72b8e4547c41c53aa40e19d3621587c80..d0627913fae854b7bb888a2fb7a84bfb752dcfee 100644
--- a/test/geomechanics/el2p/el2pproblem.hh
+++ b/test/geomechanics/el2p/el2pproblem.hh
@@ -591,9 +591,9 @@ public:
     {
         values = 0.0;
         if(initializationRun_ == false){
-        if(globalPos[0] > 490 && globalPos[0] < 510
-                        && globalPos[1] > 490 && globalPos[1] < 510
-                        && globalPos[dimWorld-1] > 490 && globalPos[dimWorld-1] < 510)
+        if(globalPos[0] > 490-eps_ && globalPos[0] < 510+eps_
+                        && globalPos[1] > 490-eps_ && globalPos[1] < 510+eps_
+                        && globalPos[dimWorld-1] > 490-eps_ && globalPos[dimWorld-1] < 510+eps_)
         values[saturationIdx] = 1.e-5; // injection
         }
     }
diff --git a/test/multidomain/2cnistokes2p2cni/stokes2cnisubproblem.hh b/test/multidomain/2cnistokes2p2cni/stokes2cnisubproblem.hh
index 2af195129031641182cfdf2c0b070febdd88da4e..0413c125ced24cd581a923fcf04531e9ba30f128 100644
--- a/test/multidomain/2cnistokes2p2cni/stokes2cnisubproblem.hh
+++ b/test/multidomain/2cnistokes2p2cni/stokes2cnisubproblem.hh
@@ -342,7 +342,7 @@ public:
         const Scalar xVelocity = xVelocity_(globalPos);
 
         if (onLeftBoundary_(globalPos)
-                && globalPos[1] > bBoxMin_[1] && globalPos[1] < bBoxMax_[1])
+                && globalPos[1] > bBoxMin_[1] - eps_ && globalPos[1] < bBoxMax_[1] + eps_)
         {
             values[transportEqIdx] = -xVelocity*density*refMassfrac();
             values[energyEqIdx] = -xVelocity*density*enthalpy;
diff --git a/test/multidomain/2cstokes2p2c/2cstokes2p2cproblem.hh b/test/multidomain/2cstokes2p2c/2cstokes2p2cproblem.hh
index 98949507864f35fbea0d7c5aaa5b337ad71ac829..d975bec88982b5e5055ea6dd11f517818b4f638c 100644
--- a/test/multidomain/2cstokes2p2c/2cstokes2p2cproblem.hh
+++ b/test/multidomain/2cstokes2p2c/2cstokes2p2cproblem.hh
@@ -177,10 +177,10 @@ public:
         {
             GlobalPosition globalPos = element.geometry().center();
 
-            if (globalPos[1] > interfacePosY_)
+            if (globalPos[1] > interfacePosY_ - eps_)
                 mdGrid.addToSubDomain(stokes2c_,element);
             else
-                if(globalPos[0] > noDarcyX_)
+                if(globalPos[0] > noDarcyX_ - eps_)
                     mdGrid.addToSubDomain(twoPtwoC_,element);
         }
         mdGrid.preUpdateSubDomains();
@@ -251,6 +251,8 @@ private:
     Scalar noDarcyX_;
     Scalar episodeLength_;
     Scalar initializationTime_;
+
+    static constexpr Scalar eps_ = 1e-8;
 };
 
 } // namespace Dumux
diff --git a/test/multidomain/2cstokes2p2c/stokes2csubproblem.hh b/test/multidomain/2cstokes2p2c/stokes2csubproblem.hh
index 1916ad4cc2b31c014363726715e7672e2a6997b8..e6e61f16bad63d1601942a01b48cfd5d6b0f4c0a 100644
--- a/test/multidomain/2cstokes2p2c/stokes2csubproblem.hh
+++ b/test/multidomain/2cstokes2p2c/stokes2csubproblem.hh
@@ -313,7 +313,7 @@ public:
         const Scalar xVelocity = xVelocity_(globalPos);
 
         if (onLeftBoundary_(globalPos)
-                && globalPos[1] > bBoxMin_[1] && globalPos[1] < bBoxMax_[1])
+                && globalPos[1] > bBoxMin_[1] - eps_ && globalPos[1] < bBoxMax_[1] + eps_)
         {
             // rho*v*X at inflow
             values[transportEqIdx] = -xVelocity * density * refMassfrac();
diff --git a/test/multidomain/2czeroeq2p2c/2czeroeq2p2cproblem.hh b/test/multidomain/2czeroeq2p2c/2czeroeq2p2cproblem.hh
index 2f1596456bbd4a1d4c9fae00ffc70174a5911984..1479aa64c5b7cc2398b843936e70da30ca20be38 100644
--- a/test/multidomain/2czeroeq2p2c/2czeroeq2p2cproblem.hh
+++ b/test/multidomain/2czeroeq2p2c/2czeroeq2p2cproblem.hh
@@ -161,10 +161,10 @@ public:
         {
             GlobalPosition globalPos = element.geometry().center();
 
-            if (globalPos[1] > interfacePosY_)
+            if (globalPos[1] > interfacePosY_ - eps_)
                 mdGrid.addToSubDomain(zeroeq2c_,element);
             else
-                if(globalPos[0] > noDarcyX_)
+                if(globalPos[0] > noDarcyX_ - eps_)
                     mdGrid.addToSubDomain(twoPtwoC_,element);
         }
         mdGrid.preUpdateSubDomains();
@@ -213,6 +213,8 @@ private:
     Scalar episodeLength_;
     Scalar initializationTime_;
     Scalar dtInit_;
+
+    static constexpr Scalar eps_ = 1e-8;
 };
 
 } // namespace Dumux
diff --git a/test/multidomain/2czeroeq2p2c/zeroeq2csubproblem.hh b/test/multidomain/2czeroeq2p2c/zeroeq2csubproblem.hh
index 6d8851e1d96bc1d15e7aaed48155703cedbfa3ef..806c1c55ebea308e2eb293f30843414f349caf21 100644
--- a/test/multidomain/2czeroeq2p2c/zeroeq2csubproblem.hh
+++ b/test/multidomain/2czeroeq2p2c/zeroeq2csubproblem.hh
@@ -268,7 +268,7 @@ public:
 
         // rho*v*X at inflow
         if (onLeftBoundary_(globalPos)
-                && globalPos[1] > bBoxMin_[1] && globalPos[1] < bBoxMax_[1])
+                && globalPos[1] > bBoxMin_[1] - eps_ && globalPos[1] < bBoxMax_[1] + eps_)
         {
             values[transportEqIdx] = -xVelocity_(globalPos) * density * refMassfrac();
         }
diff --git a/test/porousmediumflow/1p/implicit/1pniconductionproblem.hh b/test/porousmediumflow/1p/implicit/1pniconductionproblem.hh
index ae4a37cfe8008b82077f8b54dc2df555c9fe946a..3b49fd61ceefc9b7dbd50ea00b836dbf5a8d4e67 100644
--- a/test/porousmediumflow/1p/implicit/1pniconductionproblem.hh
+++ b/test/porousmediumflow/1p/implicit/1pniconductionproblem.hh
@@ -132,7 +132,6 @@ class OnePNIConductionProblem : public ImplicitPorousMediaProblem<TypeTag>
 public:
     OnePNIConductionProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-        , eps_(1e-6)
     {
         //initialize fluid system
         FluidSystem::init();
@@ -343,7 +342,7 @@ private:
     }
 
     Scalar temperatureHigh_;
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
     int outputInterval_;
 };
diff --git a/test/porousmediumflow/1p2c/implicit/1p2cniconductionproblem.hh b/test/porousmediumflow/1p2c/implicit/1p2cniconductionproblem.hh
index 0ed78b339c641277293ca523a09eb7837206aeb8..e3fe3c0b4208f57080e2d3b594caf0958c419b85 100644
--- a/test/porousmediumflow/1p2c/implicit/1p2cniconductionproblem.hh
+++ b/test/porousmediumflow/1p2c/implicit/1p2cniconductionproblem.hh
@@ -146,7 +146,6 @@ class OnePTwoCNIConductionProblem : public ImplicitPorousMediaProblem<TypeTag>
 public:
     OnePTwoCNIConductionProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-        , eps_(1e-6)
     {
         //initialize fluid system
         FluidSystem::init();
@@ -363,7 +362,7 @@ private:
     }
 
     Scalar temperatureHigh_;
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
     int outputInterval_;
 };
diff --git a/test/porousmediumflow/1p2c/implicit/1p2cniconvectionproblem.hh b/test/porousmediumflow/1p2c/implicit/1p2cniconvectionproblem.hh
index 83b0dad6ea43414781af5f858885101c7953dd6a..18165710708da951056e991015206581fa034f8d 100644
--- a/test/porousmediumflow/1p2c/implicit/1p2cniconvectionproblem.hh
+++ b/test/porousmediumflow/1p2c/implicit/1p2cniconvectionproblem.hh
@@ -145,7 +145,6 @@ class OnePTwoCNIConvectionProblem : public ImplicitPorousMediaProblem<TypeTag>
 public:
     OnePTwoCNIConvectionProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-        , eps_(1e-6)
     {
         //initialize fluid system
         FluidSystem::init();
@@ -387,7 +386,7 @@ private:
     Scalar pressureHigh_;
     Scalar pressureLow_;
     Scalar darcyVelocity_;
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
     int outputInterval_;
 };
diff --git a/test/porousmediumflow/1p2c/implicit/1p2coutflowproblem.hh b/test/porousmediumflow/1p2c/implicit/1p2coutflowproblem.hh
index 126f5e82227c6547b7161355e4d0548ad9018baa..06b547aa180e0bfd0a0e6f43de6f5569f0443cc7 100644
--- a/test/porousmediumflow/1p2c/implicit/1p2coutflowproblem.hh
+++ b/test/porousmediumflow/1p2c/implicit/1p2coutflowproblem.hh
@@ -157,7 +157,6 @@ class OnePTwoCOutflowProblem : public ImplicitPorousMediaProblem<TypeTag>
 public:
     OnePTwoCOutflowProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-        , eps_(1e-6)
     {
         //initialize fluid system
         FluidSystem::init();
@@ -338,7 +337,7 @@ private:
 #endif
     }
 
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
 };
 
diff --git a/test/porousmediumflow/2p/implicit/cc2pcornerpointproblem.hh b/test/porousmediumflow/2p/implicit/cc2pcornerpointproblem.hh
index 181628d61813a0f8c5da35e27715f084e5433fe7..a0fcee16206369c90a3f3f055b7d227abce67bad 100644
--- a/test/porousmediumflow/2p/implicit/cc2pcornerpointproblem.hh
+++ b/test/porousmediumflow/2p/implicit/cc2pcornerpointproblem.hh
@@ -132,7 +132,6 @@ public:
     : ParentType(timeManager, gridView), gravity_(0)
     {
         gravity_[dimWorld-1] = 9.81;
-        eps_ = 3e-6;
         temperature_ = 273.15 + 20; // -> 20°C
 
         name_ = GET_RUNTIME_PARAM_FROM_GROUP(TypeTag, std::string, Problem, Name);
@@ -232,7 +231,7 @@ public:
         // set no-flux on top and bottom, hydrostatic on the rest
         // use the intersection normal to decide
         const GlobalPosition normal = intersection.centerUnitOuterNormal();
-        if (std::abs(normal[dimWorld-1]) > 0.5)
+        if (std::abs(normal[dimWorld-1]) > 0.5 - eps_)
             values.setAllNeumann();
         else
             values.setAllDirichlet();
@@ -330,7 +329,7 @@ public:
 
 private:
     Scalar temperature_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 3e-6;
     std::string name_;
     GlobalPosition gravity_;
     int injectionElement_;
diff --git a/test/porousmediumflow/2p/implicit/fractureproblem.hh b/test/porousmediumflow/2p/implicit/fractureproblem.hh
index a3ca342c93d9129638f30c435ffd904861135683..63bdbf0eeb711055b68b160fe98c318177e10f1d 100644
--- a/test/porousmediumflow/2p/implicit/fractureproblem.hh
+++ b/test/porousmediumflow/2p/implicit/fractureproblem.hh
@@ -167,7 +167,6 @@ public:
     FractureProblem(TimeManager &timeManager, const GridView &gridView)
     : ParentType(timeManager, gridView)
     {
-        eps_ = 1.5e-7;
         name_ = GET_RUNTIME_PARAM_FROM_GROUP(TypeTag, std::string, Problem, Name);
     }
 
@@ -246,7 +245,7 @@ public:
 
         if (onInlet_(globalPos))
             values.setAllNeumann();
-        if (globalPos[2] > 1.0-eps_ || globalPos[2] < eps_)
+        if (globalPos[2] > 1.0 - eps_ || globalPos[2] < eps_)
             values.setAllNeumann();
     }
 
@@ -312,10 +311,10 @@ public:
 private:
     bool onInlet_(const GlobalPosition &globalPos) const
     {
-        return globalPos[0] < eps_ && globalPos[1] > -0.5;
+        return globalPos[0] < eps_ && globalPos[1] > -0.5 - eps_;
     }
 
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1.5e-7;
     std::string name_;
 };
 
diff --git a/test/porousmediumflow/2p/implicit/generalizeddirichletproblem.hh b/test/porousmediumflow/2p/implicit/generalizeddirichletproblem.hh
index 1125ced35e1daada47ed903de2031eaa5e312e6e..a43fbdf1138e06513d6cbe4b48c8ca349395ed05 100644
--- a/test/porousmediumflow/2p/implicit/generalizeddirichletproblem.hh
+++ b/test/porousmediumflow/2p/implicit/generalizeddirichletproblem.hh
@@ -113,7 +113,6 @@ public:
     GeneralizedDirichletProblem(TimeManager &timeManager,
                                 const GridView &gridView)
     : ParentType(timeManager, gridView)
-    , eps_(3e-6)
     {
         name_ = GET_RUNTIME_PARAM_FROM_GROUP(TypeTag, std::string, Problem, Name);
     }
@@ -193,7 +192,7 @@ public:
     }
 
 private:
-    Scalar eps_;
+    static constexpr Scalar eps_ = 3e-6;
     std::string name_;
 };
 }
diff --git a/test/porousmediumflow/2p/implicit/injectionproblem2pni.hh b/test/porousmediumflow/2p/implicit/injectionproblem2pni.hh
index 91521b5250fbabb10c21d7564cb2278240f6274c..eb5425cd02585522e78c3bb86029d873ab38af9d 100644
--- a/test/porousmediumflow/2p/implicit/injectionproblem2pni.hh
+++ b/test/porousmediumflow/2p/implicit/injectionproblem2pni.hh
@@ -164,7 +164,6 @@ public:
         : ParentType(timeManager, gridView)
     {
         maxDepth_ = 2700.0; // [m]
-        eps_ = 1e-6;
 
         // initialize the tables of the fluid system
         FluidSystem::init(/*tempMin=*/273.15,
@@ -291,7 +290,7 @@ public:
         else
             globalPos = intersection.geometry().center();
 
-        if (globalPos[1] < 15 && globalPos[1] > 7) {
+        if (globalPos[1] < 15 + eps_ && globalPos[1] > 7 - eps_) {
             // inject air. negative values mean injection
             values[contiNEqIdx] = -1e-3; // kg/(s*m^2)
         }
@@ -320,7 +319,7 @@ public:
 
 #if !ISOTHERMAL
         values[temperatureIdx] = 283.0 + (maxDepth_ - globalPos[1])*0.03;
-        if (globalPos[0] > 20 && globalPos[0] < 30 && globalPos[1] > 5 && globalPos[1] < 35)
+        if (globalPos[0] > 20 - eps_ && globalPos[0] < 30 + eps_ && globalPos[1] > 5 - eps_ && globalPos[1] < 35 + eps_)
             values[temperatureIdx] = 380;
 #endif // !ISOTHERMAL
     }
@@ -328,7 +327,7 @@ public:
 
 private:
     Scalar maxDepth_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1.5e-7;
     std::string name_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/2p/implicit/lensproblem.hh b/test/porousmediumflow/2p/implicit/lensproblem.hh
index 07fde62f11a827d0b6a7080203e35c6eaa1435c6..8f3d9e2c46e533a2639c6d0b28ae7fef8ef98297 100644
--- a/test/porousmediumflow/2p/implicit/lensproblem.hh
+++ b/test/porousmediumflow/2p/implicit/lensproblem.hh
@@ -211,7 +211,6 @@ public:
                 const GridView &gridView)
     : ParentType(timeManager, gridView)
     {
-        eps_ = 3e-6;
         temperature_ = 273.15 + 20; // -> 20°C
 
         name_ = GET_RUNTIME_PARAM_FROM_GROUP(TypeTag,
@@ -455,7 +454,7 @@ private:
     }
 
     Scalar temperature_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 3e-6;
     std::string name_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/2p/implicit/lensspatialparams.hh b/test/porousmediumflow/2p/implicit/lensspatialparams.hh
index 8d4b53a53e2081fd5de6fe5f169b6eb9c56b5da1..9328c180b848cd9cafd53827e256c5c6fc76390d 100644
--- a/test/porousmediumflow/2p/implicit/lensspatialparams.hh
+++ b/test/porousmediumflow/2p/implicit/lensspatialparams.hh
@@ -173,7 +173,7 @@ private:
     bool isInLens_(const GlobalPosition &globalPos) const
     {
         for (int i = 0; i < dimWorld; ++i) {
-            if (globalPos[i] < lensLowerLeft_[i] || globalPos[i] > lensUpperRight_[i])
+            if (globalPos[i] < lensLowerLeft_[i] + eps_ || globalPos[i] > lensUpperRight_[i] - eps_)
                 return false;
         }
         return true;
@@ -186,6 +186,8 @@ private:
     Scalar outerK_;
     MaterialLawParams lensMaterialParams_;
     MaterialLawParams outerMaterialParams_;
+
+    static constexpr Scalar eps_ = 1.5e-7;
 };
 
 } // end namespace
diff --git a/test/porousmediumflow/2p/sequential/test_impesadaptiveproblem.hh b/test/porousmediumflow/2p/sequential/test_impesadaptiveproblem.hh
index f24324f108b8696504a70e0d126061a571cc5199..3a45ef74c5fb43f675b966e3e15f303fc982be0b 100644
--- a/test/porousmediumflow/2p/sequential/test_impesadaptiveproblem.hh
+++ b/test/porousmediumflow/2p/sequential/test_impesadaptiveproblem.hh
@@ -144,7 +144,7 @@ class TestIMPESAdaptiveProblem: public IMPESProblem2P<TypeTag>
 
 public:
     TestIMPESAdaptiveProblem(TimeManager &timeManager, const GridView &gridView) :
-            ParentType(timeManager, gridView), eps_(1e-6)
+            ParentType(timeManager, gridView)
     {
         name_ = GET_RUNTIME_PARAM_FROM_GROUP(TypeTag, std::string, Problem, Name);
 
@@ -271,7 +271,7 @@ public:
     }
 
 private:
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/2p/sequential/test_impesproblem.hh b/test/porousmediumflow/2p/sequential/test_impesproblem.hh
index 074f2fd601786d4293af21c80cd0598b79a19fc0..5fba7a84e4e815e1f88c34c851fdcaa16853e965 100644
--- a/test/porousmediumflow/2p/sequential/test_impesproblem.hh
+++ b/test/porousmediumflow/2p/sequential/test_impesproblem.hh
@@ -163,7 +163,7 @@ typedef typename GET_PROP(TypeTag, SolutionTypes) SolutionTypes;
 
 public:
 IMPESTestProblem(TimeManager &timeManager, const GridView &gridView) :
-ParentType(timeManager, gridView), eps_(1e-6)
+ParentType(timeManager, gridView)
 {
     name_ = GET_RUNTIME_PARAM(TypeTag, std::string, Problem.Name);
 }
@@ -283,7 +283,7 @@ void initial(PrimaryVariables &values,
 
 private:
 
-const Scalar eps_;
+static constexpr Scalar eps_ = 1e-6;
 std::string name_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/2p/sequential/test_mpfa2pspatialparams.hh b/test/porousmediumflow/2p/sequential/test_mpfa2pspatialparams.hh
index bb06311da25168b2a312d943ac737259b77330b5..b2a890214c868751d882fde0b0325ff97dccd9fc 100644
--- a/test/porousmediumflow/2p/sequential/test_mpfa2pspatialparams.hh
+++ b/test/porousmediumflow/2p/sequential/test_mpfa2pspatialparams.hh
@@ -279,7 +279,7 @@ private:
     {
         for (int i = 0; i < dim; i++)
         {
-            if (globalPos[i] < lensOneLowerLeft_[i] || globalPos[i] > lensOneUpperRight_[i])
+            if (globalPos[i] < lensOneLowerLeft_[i] + eps_ || globalPos[i] > lensOneUpperRight_[i] - eps_)
             {
                 return false;
             }
@@ -290,7 +290,7 @@ private:
     {
         for (int i = 0; i < dim; i++)
         {
-            if (globalPos[i] < lensTwoLowerLeft_[i] || globalPos[i] > lensTwoUpperRight_[i])
+            if (globalPos[i] < lensTwoLowerLeft_[i] + eps_ || globalPos[i] > lensTwoUpperRight_[i] - eps_)
             {
                 return false;
             }
@@ -301,7 +301,7 @@ private:
     {
         for (int i = 0; i < dim; i++)
         {
-            if (globalPos[i] < lensThreeLowerLeft_[i] || globalPos[i] > lensThreeUpperRight_[i])
+            if (globalPos[i] < lensThreeLowerLeft_[i] + eps_ || globalPos[i] > lensThreeUpperRight_[i] - eps_)
             {
                 return false;
             }
@@ -319,6 +319,8 @@ private:
     GlobalPosition lensTwoUpperRight_;
     GlobalPosition lensThreeLowerLeft_;
     GlobalPosition lensThreeUpperRight_;
+
+    static constexpr Scalar eps_ = 1e-6;
 };
 
 } // end namespace
diff --git a/test/porousmediumflow/2p/sequential/test_transportproblem.hh b/test/porousmediumflow/2p/sequential/test_transportproblem.hh
index 5cfc6e108c90060cfe93721e6fd2185063780429..b833a0d3c0a4ce7e0e3f66dcbe7d38f5cc64e204 100644
--- a/test/porousmediumflow/2p/sequential/test_transportproblem.hh
+++ b/test/porousmediumflow/2p/sequential/test_transportproblem.hh
@@ -122,7 +122,7 @@ class TestTransportProblem: public TransportProblem2P<TypeTag>
 
 public:
     TestTransportProblem(TimeManager &timeManager, const GridView &gridView) :
-        ParentType(timeManager, gridView), eps_(1e-6)
+        ParentType(timeManager, gridView)
     {}
 
 
@@ -251,7 +251,7 @@ public:
     }
 
 private:
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
 };
 } //end namespace
 
diff --git a/test/porousmediumflow/2p1c/implicit/steaminjectionproblem.hh b/test/porousmediumflow/2p1c/implicit/steaminjectionproblem.hh
index 27f692e876663a57444883c988e370a7d5cc6a4d..97a3347bd0eba5a200f2ec79e9a2983240d388ad 100644
--- a/test/porousmediumflow/2p1c/implicit/steaminjectionproblem.hh
+++ b/test/porousmediumflow/2p1c/implicit/steaminjectionproblem.hh
@@ -133,7 +133,7 @@ public:
      */
 
     InjectionProblem(TimeManager &timeManager, const GridView &gridView)
-        : ParentType(timeManager, gridView), eps_(1e-6)
+        : ParentType(timeManager, gridView)
     {
 
         name_ = GET_RUNTIME_PARAM_FROM_GROUP(TypeTag,
@@ -273,7 +273,7 @@ private:
         values[switch1Idx] = 283.13;
     }
 
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/2p2c/implicit/injectionproblem.hh b/test/porousmediumflow/2p2c/implicit/injectionproblem.hh
index 86c6f454b8ebf6ba9c9d8039c962d9cd57a285f1..23e41f822c2bafc7af742462805dcbc78febba5e 100644
--- a/test/porousmediumflow/2p2c/implicit/injectionproblem.hh
+++ b/test/porousmediumflow/2p2c/implicit/injectionproblem.hh
@@ -160,9 +160,6 @@ public:
          * - Overwriting on command line not possible
          */
 
-
-        eps_ = 1e-6;
-
         // initialize the tables of the fluid system
         FluidSystem::init(/*Tmin=*/temperatureLow_,
                           /*Tmax=*/temperatureHigh_,
@@ -383,7 +380,7 @@ private:
 
     Scalar temperature_;
     Scalar depthBOR_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
 
     int nTemperature_;
     int nPressure_;
diff --git a/test/porousmediumflow/2p2c/implicit/waterairproblem.hh b/test/porousmediumflow/2p2c/implicit/waterairproblem.hh
index cb9283d6d36afd10785f596d15a3f13f0f74690a..5fee95755f2436e78c6b01a7d4f74d1939598ecb 100644
--- a/test/porousmediumflow/2p2c/implicit/waterairproblem.hh
+++ b/test/porousmediumflow/2p2c/implicit/waterairproblem.hh
@@ -156,7 +156,6 @@ public:
         : ParentType(timeManager, gridView)
     {
         maxDepth_ = 1000.0; // [m]
-        eps_ = 1e-6;
 
         FluidSystem::init();
 
@@ -291,7 +290,7 @@ public:
             globalPos = intersection.geometry().center();
 
         // negative values for injection
-        if (globalPos[0] > 15 && globalPos[0] < 25 &&
+        if (globalPos[0] > 15 - eps_ && globalPos[0] < 25 + eps_ &&
             globalPos[1] < eps_)
         {
             values[contiNEqIdx] = -1e-3/FluidSystem::molarMass(nCompIdx); //(kg/(m^2*s) or mole/(m^2*s) )
@@ -319,7 +318,7 @@ public:
         initial_(values, globalPos);
 
 #if !ISOTHERMAL
-        if (globalPos[0] > 20 && globalPos[0] < 30 && globalPos[1] < 30)
+        if (globalPos[0] > 20 - eps_ && globalPos[0] < 30 + eps_ && globalPos[1] < 30 + eps_)
             values[temperatureIdx] = 380;
 #endif
     }
@@ -353,7 +352,7 @@ private:
     }
 
     Scalar maxDepth_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/2p2c/sequential/test_adaptive2p2c2dproblem.hh b/test/porousmediumflow/2p2c/sequential/test_adaptive2p2c2dproblem.hh
index e3293ca7de29e12463cb02ffa2583f8df1ba4e75..c66fca6f71be0c830d20cd0591cd2ce4cabab7ba 100644
--- a/test/porousmediumflow/2p2c/sequential/test_adaptive2p2c2dproblem.hh
+++ b/test/porousmediumflow/2p2c/sequential/test_adaptive2p2c2dproblem.hh
@@ -174,7 +174,7 @@ Scalar referencePressureAtPos(const GlobalPosition& globalPos) const
  */
 void boundaryTypesAtPos(BoundaryTypes &bcTypes, const GlobalPosition& globalPos) const
 {
-    if (globalPos[0] > this->bBoxMax()[0]-1E-6 || globalPos[0] < 1e-6)
+    if (globalPos[0] > this->bBoxMax()[0] - eps_|| globalPos[0] < eps_)
         bcTypes.setAllDirichlet();
     else
         // all other boundaries
@@ -198,7 +198,7 @@ void dirichletAtPos(PrimaryVariables &bcValues, const GlobalPosition& globalPos)
     Scalar temp = temperatureAtPos(globalPos);
 
     // Dirichlet for pressure equation
-    bcValues[Indices::pressureEqIdx] = (globalPos[0] < 1e-6) ? (2.5e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1])
+    bcValues[Indices::pressureEqIdx] = (globalPos[0] < eps_) ? (2.5e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1])
             : (2e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1]);
 
     // Dirichlet values for transport equations
@@ -228,7 +228,7 @@ void source(PrimaryVariables &values, const Element &element)
         father = father.father();
     }
     GlobalPosition globalPos = father.geometry().center();
-    if (fabs(globalPos[0] - 4.8) < 0.5 && fabs(globalPos[1] - 4.8) < 0.5)
+    if (fabs(globalPos[0] - 4.8) < 0.5 + eps_ && fabs(globalPos[1] - 4.8) < 0.5 + eps_)
         values[Indices::contiNEqIdx] = 0.0001;
 }
 
@@ -251,6 +251,7 @@ Scalar initConcentrationAtPos(const GlobalPosition& globalPos) const
 private:
 //Grid grid_;
 VtkMultiWriter<GridView> debugWriter_;
+static constexpr Scalar eps_ = 1e-6;
 };
 } //end namespace
 
diff --git a/test/porousmediumflow/2p2c/sequential/test_adaptive2p2c3dproblem.hh b/test/porousmediumflow/2p2c/sequential/test_adaptive2p2c3dproblem.hh
index d29abda775ea441ddac5da0f293d0e8cf924f57e..b59679b444e5200999b730b1bb3e75eef5a6ff8b 100644
--- a/test/porousmediumflow/2p2c/sequential/test_adaptive2p2c3dproblem.hh
+++ b/test/porousmediumflow/2p2c/sequential/test_adaptive2p2c3dproblem.hh
@@ -186,7 +186,7 @@ Scalar referencePressureAtPos(const GlobalPosition& globalPos) const
  */
 void boundaryTypesAtPos(BoundaryTypes &bcTypes, const GlobalPosition& globalPos) const
 {
-    if (globalPos[0] > 10-1E-6 || globalPos[0] < 1e-6)
+    if (globalPos[0] > 10 - eps_ || globalPos[0] < eps_)
         bcTypes.setAllDirichlet();
     else
         // all other boundaries
@@ -210,7 +210,7 @@ void dirichletAtPos(PrimaryVariables &bcValues, const GlobalPosition& globalPos)
     Scalar temp = temperatureAtPos(globalPos);
 
     // Dirichlet for pressure equation
-    bcValues[Indices::pressureEqIdx] = (globalPos[0] < 1e-6) ? (2.5e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1])
+    bcValues[Indices::pressureEqIdx] = (globalPos[0] < eps_) ? (2.5e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1])
             : (2e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1]);
 
     // Dirichlet values for transport equations
@@ -232,7 +232,7 @@ void neumannAtPos(PrimaryVariables &neumannValues, const GlobalPosition& globalP
 void sourceAtPos(PrimaryVariables &sourceValues, const GlobalPosition& globalPos) const
 {
     this->setZero(sourceValues);
-    if (fabs(globalPos[0] - 4.8) < 0.5 && fabs(globalPos[1] - 4.8) < 0.5)
+    if (fabs(globalPos[0] - 4.8) < 0.5 + eps_ && fabs(globalPos[1] - 4.8) < 0.5 + eps_)
         sourceValues[Indices::contiNEqIdx] = injectionrate_;
 }
 
@@ -255,6 +255,7 @@ Scalar initConcentrationAtPos(const GlobalPosition& globalPos) const
 private:
 VtkMultiWriter<GridView> debugWriter_;
 Scalar injectionrate_;
+static constexpr Scalar eps_ = 1e-6;
 };
 } //end namespace
 
diff --git a/test/porousmediumflow/2p2c/sequential/test_dec2p2cproblem.hh b/test/porousmediumflow/2p2c/sequential/test_dec2p2cproblem.hh
index 012d38f6b85f72742e26b8fcdc6439613ff1ef0c..f2d09ca79fd9b730cc8248e26f38837513c4ebca 100644
--- a/test/porousmediumflow/2p2c/sequential/test_dec2p2cproblem.hh
+++ b/test/porousmediumflow/2p2c/sequential/test_dec2p2cproblem.hh
@@ -114,7 +114,7 @@ typedef Dune::FieldVector<Scalar, dimWorld> GlobalPosition;
 
 public:
 TestDecTwoPTwoCProblem(TimeManager &timeManager, const GridView &gridView) :
-ParentType(timeManager, gridView), eps_(1e-6), depthBOR_(1000.0)
+ParentType(timeManager, gridView), depthBOR_(1000.0)
 {}
 
 /*!
@@ -168,7 +168,7 @@ Scalar referencePressureAtPos(const GlobalPosition& globalPos) const
  */
 void boundaryTypesAtPos(BoundaryTypes &bcTypes, const GlobalPosition& globalPos) const
 {
-    if (globalPos[0] > this->bBoxMax()[0]-1E-6 || globalPos[0] < 1e-6)
+    if (globalPos[0] > this->bBoxMax()[0] - eps_ || globalPos[0] < eps_)
         bcTypes.setAllDirichlet();
     else
         // all other boundaries
@@ -202,7 +202,7 @@ void dirichletAtPos(PrimaryVariables &bcValues ,const GlobalPosition& globalPos)
     Scalar temp = temperatureAtPos(globalPos);
 
     // Dirichlet for pressure equation
-    bcValues[Indices::pressureEqIdx] = (globalPos[0] < 1e-6) ? (2.5e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1])
+    bcValues[Indices::pressureEqIdx] = (globalPos[0] < eps_) ? (2.5e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1])
             : (2e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1]);
 
     // Dirichlet values for transport equations
@@ -239,7 +239,7 @@ void neumannAtPos(PrimaryVariables &neumannValues, const GlobalPosition& globalP
 void sourceAtPos(PrimaryVariables &sourceValues, const GlobalPosition& globalPos) const
 {
     this->setZero(sourceValues);
-    if (fabs(globalPos[0] - 4.8) < 0.5 && fabs(globalPos[1] - 4.8) < 0.5)
+    if (fabs(globalPos[0] - 4.8) < 0.5 + eps_ && fabs(globalPos[1] - 4.8) < 0.5 + eps_)
         sourceValues[Indices::contiNEqIdx] = 0.0001;
 }
 //! Flag for the type of initial conditions
@@ -262,7 +262,7 @@ private:
 GlobalPosition lowerLeft_;
 GlobalPosition upperRight_;
 
-const Scalar eps_;
+static constexpr Scalar eps_ = 1e-6;
 const Scalar depthBOR_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/2p2c/sequential/test_multiphysics2p2cproblem.hh b/test/porousmediumflow/2p2c/sequential/test_multiphysics2p2cproblem.hh
index a68e9097e6afa95daafc30ec1ee248132f8c0e95..31b4affa42aa49de1ed362a041314bbe1bba44e7 100644
--- a/test/porousmediumflow/2p2c/sequential/test_multiphysics2p2cproblem.hh
+++ b/test/porousmediumflow/2p2c/sequential/test_multiphysics2p2cproblem.hh
@@ -124,7 +124,7 @@ typedef Dune::FieldVector<Scalar, dimWorld> GlobalPosition;
 
 public:
 TestMultTwoPTwoCProblem(TimeManager &timeManager, const GridView &gridView, const GlobalPosition upperRight = 0) :
-ParentType(timeManager, gridView), lowerLeft_(0), upperRight_(upperRight), eps_(1e-6), depthBOR_(1000.0)
+ParentType(timeManager, gridView), lowerLeft_(0), upperRight_(upperRight), depthBOR_(1000.0)
 {}
 
 /*!
@@ -169,7 +169,7 @@ Scalar referencePressureAtPos(const GlobalPosition& globalPos) const
  */
 void boundaryTypesAtPos(BoundaryTypes &bcTypes, const GlobalPosition& globalPos) const
 {
-    if (globalPos[0] > 10-1E-6 || globalPos[0] < 1e-6)
+    if (globalPos[0] > 10 - eps_ || globalPos[0] < eps_)
         bcTypes.setAllDirichlet();
     else
         // all other boundaries
@@ -192,7 +192,7 @@ void dirichletAtPos(PrimaryVariables &bcValues ,const GlobalPosition& globalPos)
     Scalar temp = temperatureAtPos(globalPos);
 
     // Dirichlet for pressure equation
-    bcValues[Indices::pressureEqIdx] = (globalPos[0] < 1e-6) ? (2.5e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1])
+    bcValues[Indices::pressureEqIdx] = (globalPos[0] < eps_) ? (2.5e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1])
             : (2e5 - FluidSystem::H2O::liquidDensity(temp, pRef) * this->gravity()[dim-1]);
 
     // Dirichlet values for transport equations
@@ -214,7 +214,7 @@ void neumannAtPos(PrimaryVariables &neumannValues, const GlobalPosition& globalP
 void sourceAtPos(PrimaryVariables &sourceValues, const GlobalPosition& globalPos) const
 {
     this->setZero(sourceValues);
-    if (fabs(globalPos[0] - 4.8) < 0.5 && fabs(globalPos[1] - 4.8) < 0.5)
+    if (fabs(globalPos[0] - 4.8) < 0.5 + eps_ && fabs(globalPos[1] - 4.8) < 0.5 + eps_)
         sourceValues[Indices::contiNEqIdx] = 0.0001;
 }
 /*!
@@ -236,7 +236,7 @@ private:
 GlobalPosition lowerLeft_;
 GlobalPosition upperRight_;
 
-const Scalar eps_;
+static constexpr Scalar eps_ = 1e-6;
 const Scalar depthBOR_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/2pdfm/implicit/2pdfmtestproblem.hh b/test/porousmediumflow/2pdfm/implicit/2pdfmtestproblem.hh
index 8f4af3e86a09b323dba024b76e8cd46c7f506fe7..0dc4fbee5be9a5eda9816acc141303ca0b0e1d88 100644
--- a/test/porousmediumflow/2pdfm/implicit/2pdfmtestproblem.hh
+++ b/test/porousmediumflow/2pdfm/implicit/2pdfmtestproblem.hh
@@ -145,7 +145,6 @@ public:
         : ParentType(timeManager, gridView),
           useInterfaceCondition_(true)
     {
-        eps_ = 3e-6;
         temperature_ = 273.15 + 20; // -> 20°C
     }
 
@@ -347,7 +346,7 @@ private:
     }
 
     Scalar temperature_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 3e-6;
 
     bool useInterfaceCondition_;
 };
diff --git a/test/porousmediumflow/2pminc/implicit/2pminctestproblem.hh b/test/porousmediumflow/2pminc/implicit/2pminctestproblem.hh
index e56c665755abd21cc6ee9fe02bbd86925ffc3f27..5d11097dcd2f0d5984c6c4d97278e8ebceb77ecd 100644
--- a/test/porousmediumflow/2pminc/implicit/2pminctestproblem.hh
+++ b/test/porousmediumflow/2pminc/implicit/2pminctestproblem.hh
@@ -179,7 +179,6 @@ public:
                 const GridView &gridView)
     : ParentType(timeManager, gridView)
     {
-        eps_ = 3e-6;
         temperature_ = 273.15 + 20; // -> 20°C
 
         name_ = GET_RUNTIME_PARAM_FROM_GROUP(TypeTag, std::string, Problem, Name);
@@ -378,7 +377,7 @@ private:
     }
 
     Scalar temperature_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 3e-6;
     std::string name_;
 };
 
diff --git a/test/porousmediumflow/2pnc/implicit/fuelcellproblem.hh b/test/porousmediumflow/2pnc/implicit/fuelcellproblem.hh
index 0ddbdf3c2f2dc5cce166d4e4cefe8fc11a174fab..9d4d1f2aa4fab74b48dfbde56b31ed5e3f1383f8 100644
--- a/test/porousmediumflow/2pnc/implicit/fuelcellproblem.hh
+++ b/test/porousmediumflow/2pnc/implicit/fuelcellproblem.hh
@@ -151,8 +151,6 @@ public:
 
         pO2Inlet_            = GET_RUNTIME_PARAM_FROM_GROUP(TypeTag, Scalar, ElectroChemistry, pO2Inlet);
 
-        eps_ = 1e-6;
-
         FluidSystem::init(/*Tmin=*/temperatureLow_,
                           /*Tmax=*/temperatureHigh_,
                           /*nT=*/nTemperature_,
@@ -394,7 +392,7 @@ private:
     { return globalPos[1] < 0.1*(this->bBoxMax()[1] - this->bBoxMin()[1]) + eps_; }
 
     Scalar temperature_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     int nTemperature_;
     int nPressure_;
     std::string name_ ;
diff --git a/test/porousmediumflow/2pnc/implicit/fuelcellspatialparams.hh b/test/porousmediumflow/2pnc/implicit/fuelcellspatialparams.hh
index 55eab512b61ee623a81cbb2d9349e4ac6768ae5a..a6c9776e7157b7f5dbcd85befd911bee4f358b46 100644
--- a/test/porousmediumflow/2pnc/implicit/fuelcellspatialparams.hh
+++ b/test/porousmediumflow/2pnc/implicit/fuelcellspatialparams.hh
@@ -122,8 +122,6 @@ public:
         //parameters for the vanGenuchten law
         materialParams_.setVgAlpha(6.66e-5); // alpha = 1/pcb
         materialParams_.setVgn(3.652);
-
-        eps_ = 1e-6;
     }
 
     ~FuelCellSpatialParams()
@@ -180,7 +178,7 @@ public:
 private:
     DimMatrix K_;
     Scalar porosity_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     MaterialLawParams materialParams_;
 };
 
diff --git a/test/porousmediumflow/2pncmin/implicit/dissolutionproblem.hh b/test/porousmediumflow/2pncmin/implicit/dissolutionproblem.hh
index c6c2046e3aa87eae0fa90635be4f7ea3072b1525..73f73ba8c60d4650eea61e1080da92c9318dd5fe 100644
--- a/test/porousmediumflow/2pncmin/implicit/dissolutionproblem.hh
+++ b/test/porousmediumflow/2pncmin/implicit/dissolutionproblem.hh
@@ -298,7 +298,7 @@ public:
         values[pressureIdx] = reservoirPressure_;
         values[switchIdx]   = initLiqSaturation_;                 // Sl primary variable
         values[xlNaClIdx]   = massTomoleFrac_(outerSalinity_);     // mole fraction
-        if(globalPos[0] > 5.0 - eps_ && globalPos[0] < 20.0 - eps_)
+        if(globalPos[0] > 5.0 - eps_ && globalPos[0] < 19.0 + eps_)
             values[precipNaClIdx] = initPrecipitatedSalt2_; // [kg/m^3]
         else
             values[precipNaClIdx] = initPrecipitatedSalt1_; // [kg/m^3]
diff --git a/test/porousmediumflow/3p/implicit/3pniconductionproblem.hh b/test/porousmediumflow/3p/implicit/3pniconductionproblem.hh
index ae8ea1c7d5204340ae758549026da59141f83a29..2c36f27c7787384a5fbf010506b1c23e1c2f9be4 100644
--- a/test/porousmediumflow/3p/implicit/3pniconductionproblem.hh
+++ b/test/porousmediumflow/3p/implicit/3pniconductionproblem.hh
@@ -135,7 +135,6 @@ class ThreePNIConductionProblem : public ImplicitPorousMediaProblem<TypeTag>
 public:
     ThreePNIConductionProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-        , eps_(1e-6)
     {
         //initialize fluid system
         FluidSystem::init();
@@ -357,7 +356,7 @@ private:
     }
 
     Scalar temperatureHigh_;
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
     int outputInterval_;
 };
diff --git a/test/porousmediumflow/3p/implicit/3pniconvectionproblem.hh b/test/porousmediumflow/3p/implicit/3pniconvectionproblem.hh
index 980403cbd8612fd5edccf33bb7864316b8a8da95..37e98b3719d61ad78562ed9bb8afb932f893ecfa 100644
--- a/test/porousmediumflow/3p/implicit/3pniconvectionproblem.hh
+++ b/test/porousmediumflow/3p/implicit/3pniconvectionproblem.hh
@@ -135,7 +135,6 @@ class ThreePNIConvectionProblem : public ImplicitPorousMediaProblem<TypeTag>
 public:
     ThreePNIConvectionProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-        , eps_(1e-6)
     {
         //initialize fluid system
         FluidSystem::init();
@@ -381,7 +380,7 @@ private:
     Scalar pressureHigh_;
     Scalar pressureLow_;
     Scalar darcyVelocity_;
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
     int outputInterval_;
 };
diff --git a/test/porousmediumflow/3p/implicit/infiltration3pproblem.hh b/test/porousmediumflow/3p/implicit/infiltration3pproblem.hh
index 5555760247e0cb1088ca557e568bbfbeb78b997d..aa5aad931d550183d2e53dd47f8f4d457d93f7d8 100644
--- a/test/porousmediumflow/3p/implicit/infiltration3pproblem.hh
+++ b/test/porousmediumflow/3p/implicit/infiltration3pproblem.hh
@@ -137,7 +137,6 @@ public:
      */
     InfiltrationThreePProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-        , eps_(1e-6)
     {
         temperature_ = 273.15 + 10.0; // -> 10 degrees Celsius
         FluidSystem::init(282.15, 284.15, 3, 8e4, 3e5, 200);
@@ -224,7 +223,7 @@ public:
         Scalar x = globalPos[0];
         Scalar sw, swr=0.12, sgr=0.03;
 
-        if(y >(-1.E-3*x+5) )
+        if(y > (-1.E-3*x+5) - eps_)
         {
             Scalar pc = 9.81 * 1000.0 * (y - (-5E-4*x+5));
             if (pc < 0.0) pc = 0.0;
@@ -276,7 +275,7 @@ public:
         // negative values for injection
         if (this->timeManager().time()<2592000.)
         {
-            if ((globalPos[0] <= 175.+eps_) && (globalPos[0] >= 150.+eps_) && (globalPos[1] >= 10.-eps_))
+            if ((globalPos[0] <= 175.+eps_) && (globalPos[0] >= 155.-eps_) && (globalPos[1] >= 10.-eps_))
             {
                 values[Indices::contiWEqIdx] = -0.0;
                 values[Indices::contiNEqIdx] = -0.001, // /*Molfluss, umr. über M(Mesit.)=0,120 kg/mol --> 1.2e-4  kg/(sm)
@@ -324,7 +323,7 @@ private:
         Scalar x = globalPos[0];
         Scalar sw, swr=0.12, sgr=0.03;
 
-        if(y >(-1.E-3*x+5) )
+        if(y > (-1.E-3*x+5) - eps_)
         {
             Scalar pc = 9.81 * 1000.0 * (y - (-5E-4*x+5));
             if (pc < 0.0) pc = 0.0;
@@ -372,7 +371,7 @@ private:
     }
 
     Scalar temperature_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/3p/implicit/infiltration3pspatialparams.hh b/test/porousmediumflow/3p/implicit/infiltration3pspatialparams.hh
index 4f5505221162019bd4d539905480ef82ca1ca169..8755c205dea7a2b765ed7039593238ce6437d352 100644
--- a/test/porousmediumflow/3p/implicit/infiltration3pspatialparams.hh
+++ b/test/porousmediumflow/3p/implicit/infiltration3pspatialparams.hh
@@ -194,8 +194,8 @@ public:
 private:
     bool isFineMaterial_(const GlobalPosition &globalPos) const
     { return
-            70. <= globalPos[0] && globalPos[0] <= 85. &&
-            7.0 <= globalPos[1] && globalPos[1] <= 7.50;
+            70. - eps_ <= globalPos[0] && globalPos[0] <= 85. + eps_ &&
+            7.0 - eps_ <= globalPos[1] && globalPos[1] <= 7.50 + eps_;
     }
 
     Scalar fineK_;
@@ -206,6 +206,8 @@ private:
     MaterialLawParams materialParams_;
 
     bool plotFluidMatrixInteractions_;
+
+    static constexpr Scalar eps_ = 1e-6;
 };
 
 }
diff --git a/test/porousmediumflow/3p3c/implicit/columnxylolproblem.hh b/test/porousmediumflow/3p3c/implicit/columnxylolproblem.hh
index 34dc848fa4c503bce8b6a4e2209f5b42445d7c7c..2f7313849d03d8e883d44f3bc6e5eef22fff72f4 100644
--- a/test/porousmediumflow/3p3c/implicit/columnxylolproblem.hh
+++ b/test/porousmediumflow/3p3c/implicit/columnxylolproblem.hh
@@ -136,7 +136,7 @@ public:
      * \param gridView The grid view
      */
     ColumnProblem(TimeManager &timeManager, const GridView &gridView)
-        : ParentType(timeManager, gridView), eps_(1e-6)
+        : ParentType(timeManager, gridView)
     {
         FluidSystem::init();
 
@@ -318,51 +318,51 @@ private:
 
         if (y > 1.2 - eps_)
             values[switch2Idx] = 0.112;
-        else if (y > 1.2 - 0.0148)
+        else if (y > 1.2 - 0.0148 - eps_)
             values[switch2Idx] = 0 + ((1.2 - y)/0.0148)*0.112;
-        else if (y > 1.2 - 0.0296)
+        else if (y > 1.2 - 0.0296 - eps_)
             values[switch2Idx] = 0.112 + (((1.2 - y) - 0.0148)/0.0148)*(0.120 - 0.112);
-        else if (y > 1.2 - 0.0444)
+        else if (y > 1.2 - 0.0444 - eps_)
             values[switch2Idx] = 0.120 + (((1.2 - y) - 0.0296)/0.0148)*(0.125 - 0.120);
-        else if (y > 1.2 - 0.0592)
+        else if (y > 1.2 - 0.0592 - eps_)
             values[switch2Idx] = 0.125 + (((1.2 - y) - 0.0444)/0.0148)*(0.137 - 0.125);
-        else if (y > 1.2 - 0.0740)
+        else if (y > 1.2 - 0.0740 - eps_)
             values[switch2Idx] = 0.137 + (((1.2 - y) - 0.0592)/0.0148)*(0.150 - 0.137);
-        else if (y > 1.2 - 0.0888)
+        else if (y > 1.2 - 0.0888 - eps_)
             values[switch2Idx] = 0.150 + (((1.2 - y) - 0.0740)/0.0148)*(0.165 - 0.150);
-        else if (y > 1.2 - 0.1036)
+        else if (y > 1.2 - 0.1036 - eps_)
             values[switch2Idx] = 0.165 + (((1.2 - y) - 0.0888)/0.0148)*(0.182 - 0.165);
-        else if (y > 1.2 - 0.1184)
+        else if (y > 1.2 - 0.1184 - eps_)
             values[switch2Idx] = 0.182 + (((1.2 - y) - 0.1036)/0.0148)*(0.202 - 0.182);
-        else if (y > 1.2 - 0.1332)
+        else if (y > 1.2 - 0.1332 - eps_)
             values[switch2Idx] = 0.202 + (((1.2 - y) - 0.1184)/0.0148)*(0.226 - 0.202);
-        else if (y > 1.2 - 0.1480)
+        else if (y > 1.2 - 0.1480 - eps_)
             values[switch2Idx] = 0.226 + (((1.2 - y) - 0.1332)/0.0148)*(0.257 - 0.226);
-        else if (y > 1.2 - 0.1628)
+        else if (y > 1.2 - 0.1628 - eps_)
             values[switch2Idx] = 0.257 + (((1.2 - y) - 0.1480)/0.0148)*(0.297 - 0.257);
-        else if (y > 1.2 - 0.1776)
+        else if (y > 1.2 - 0.1776 - eps_)
             values[switch2Idx] = 0.297 + (((1.2 - y) - 0.1628)/0.0148)*(0.352 - 0.297);
-        else if (y > 1.2 - 0.1924)
+        else if (y > 1.2 - 0.1924 - eps_)
             values[switch2Idx] = 0.352 + (((1.2 - y) - 0.1776)/0.0148)*(0.426 - 0.352);
-        else if (y > 1.2 - 0.2072)
+        else if (y > 1.2 - 0.2072 - eps_)
             values[switch2Idx] = 0.426 + (((1.2 - y) - 0.1924)/0.0148)*(0.522 - 0.426);
-        else if (y > 1.2 - 0.2220)
+        else if (y > 1.2 - 0.2220 - eps_)
             values[switch2Idx] = 0.522 + (((1.2 - y) - 0.2072)/0.0148)*(0.640 - 0.522);
-        else if (y > 1.2 - 0.2368)
+        else if (y > 1.2 - 0.2368 - eps_)
             values[switch2Idx] = 0.640 + (((1.2 - y) - 0.2220)/0.0148)*(0.767 - 0.640);
-        else if (y > 1.2 - 0.2516)
+        else if (y > 1.2 - 0.2516 - eps_)
             values[switch2Idx] = 0.767 + (((1.2 - y) - 0.2368)/0.0148)*(0.878 - 0.767);
-        else if (y > 1.2 - 0.2664)
+        else if (y > 1.2 - 0.2664 - eps_)
             values[switch2Idx] = 0.878 + (((1.2 - y) - 0.2516)/0.0148)*(0.953 - 0.878);
-        else if (y > 1.2 - 0.2812)
+        else if (y > 1.2 - 0.2812 - eps_)
             values[switch2Idx] = 0.953 + (((1.2 - y) - 0.2664)/0.0148)*(0.988 - 0.953);
-        else if (y > 1.2 - 0.3000)
+        else if (y > 1.2 - 0.3000 - eps_)
             values[switch2Idx] = 0.988;
         else
             values[switch2Idx] = 1.e-4;
     }
 
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/3p3c/implicit/columnxylolspatialparams.hh b/test/porousmediumflow/3p3c/implicit/columnxylolspatialparams.hh
index cb83c878028a39ab31a0508cd816df69dc65fe6b..3aa624a6f830df7e5b350d42431a878235880824 100644
--- a/test/porousmediumflow/3p3c/implicit/columnxylolspatialparams.hh
+++ b/test/porousmediumflow/3p3c/implicit/columnxylolspatialparams.hh
@@ -272,7 +272,7 @@ public:
 private:
     bool isFineMaterial_(const GlobalPosition &globalPos) const
     {
-        if (0.90 <= globalPos[1])
+        if (0.90 - eps_ <= globalPos[1])
             return true;
         else return false;
     }
@@ -290,6 +290,8 @@ private:
     MaterialLawParams coarseMaterialParams_;
 
     Scalar lambdaSolid_;
+
+    static constexpr Scalar eps_ = 1e-6;
 };
 
 }
diff --git a/test/porousmediumflow/3p3c/implicit/infiltrationproblem.hh b/test/porousmediumflow/3p3c/implicit/infiltrationproblem.hh
index 1ed8fede28f2e7d6dc09cd5108587be7fdf95bcb..feec2c4e298e1f6643289da902df2dd53eadc7de 100644
--- a/test/porousmediumflow/3p3c/implicit/infiltrationproblem.hh
+++ b/test/porousmediumflow/3p3c/implicit/infiltrationproblem.hh
@@ -150,7 +150,6 @@ public:
      */
     InfiltrationProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-        , eps_(1e-6)
     {
         temperature_ = 273.15 + 10.0; // -> 10 degrees Celsius
         FluidSystem::init(/*tempMin=*/temperature_ - 1,
@@ -240,7 +239,7 @@ public:
         Scalar x = globalPos[0];
         Scalar sw, swr=0.12, sgr=0.03;
 
-        if(y >(-1.E-3*x+5) )
+        if(y >(-1.E-3*x+5) - eps_)
         {
             Scalar pc = 9.81 * 1000.0 * (y - (-5E-4*x+5));
             if (pc < 0.0) pc = 0.0;
@@ -290,7 +289,7 @@ public:
             globalPos = intersection.geometry().center();
 
         // negative values for injection
-        if ((globalPos[0] <= 75.+eps_) && (globalPos[0] >= 50.+eps_) && (globalPos[1] >= 10.-eps_))
+        if ((globalPos[0] <= 75.+eps_) && (globalPos[0] >= 55.-eps_) && (globalPos[1] >= 10.-eps_))
         {
             values[contiWEqIdx] = -0.0;
             values[contiNEqIdx] = -0.001, //mole flow, convertion to mass flow with molar mass M(Mesit.)=0,120 kg/mol --> 1.2e-4 kg/(sm)
@@ -372,7 +371,7 @@ private:
         Scalar x = globalPos[0];
         Scalar sw, swr=0.12, sgr=0.03;
 
-        if(y >(-1.E-3*x+5) )
+        if(y >(-1.E-3*x+5) - eps_)
         {
             Scalar pc = 9.81 * 1000.0 * (y - (-5E-4*x+5));
             if (pc < 0.0) pc = 0.0;
@@ -420,7 +419,7 @@ private:
     }
 
     Scalar temperature_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/3p3c/implicit/kuevetteproblem.hh b/test/porousmediumflow/3p3c/implicit/kuevetteproblem.hh
index 6011dfe66e3d249458bff202af58ee83f2f3d29e..87800c0683a7f6b68641cf4ee75e92875dad9be4 100644
--- a/test/porousmediumflow/3p3c/implicit/kuevetteproblem.hh
+++ b/test/porousmediumflow/3p3c/implicit/kuevetteproblem.hh
@@ -150,7 +150,7 @@ public:
      * \param gridView The grid view
      */
     KuevetteProblem(TimeManager &timeManager, const GridView &gridView)
-        : ParentType(timeManager, gridView), eps_(1e-6)
+        : ParentType(timeManager, gridView)
     {
         FluidSystem::init();
 
@@ -357,7 +357,7 @@ private:
         }
     }
 
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
     Scalar episodeLength_;
 };
diff --git a/test/porousmediumflow/3pwateroil/implicit/3pwateroilsagdproblem.hh b/test/porousmediumflow/3pwateroil/implicit/3pwateroilsagdproblem.hh
index 2953d9eed8bcc074b942ded26fe3a8ef03ad4580..db13834c0a28391dde9fb46ac4cd7c01097c400d 100644
--- a/test/porousmediumflow/3pwateroil/implicit/3pwateroilsagdproblem.hh
+++ b/test/porousmediumflow/3pwateroil/implicit/3pwateroilsagdproblem.hh
@@ -141,7 +141,7 @@ public:
      */
 
     SagdProblem(TimeManager &timeManager, const GridView &gridView)
-        : ParentType(timeManager, gridView), eps_(1e-6), pOut_(4e6)
+        : ParentType(timeManager, gridView), pOut_(4e6)
     {
 
         maxDepth_ = 400.0; // [m]
@@ -430,7 +430,7 @@ private:
     }
 
     Scalar maxDepth_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     Scalar pIn_;
     Scalar pOut_;
     Scalar totalMassProducedOil_;
diff --git a/test/porousmediumflow/co2/implicit/heterogeneousproblem.hh b/test/porousmediumflow/co2/implicit/heterogeneousproblem.hh
index 155955e493700cec3bef0e14d4d9c7f68e481f4d..dd260e8cc7e08355632daa16a3706f5889b4e5d4 100644
--- a/test/porousmediumflow/co2/implicit/heterogeneousproblem.hh
+++ b/test/porousmediumflow/co2/implicit/heterogeneousproblem.hh
@@ -192,8 +192,6 @@ public:
         // set the spatial parameters by reading the DGF grid file
         this->spatialParams().setParams();
 
-        eps_ = 1e-6;
-
         // initialize the tables of the fluid system
         FluidSystem::init(/*Tmin=*/temperatureLow_,
                           /*Tmax=*/temperatureHigh_,
@@ -489,7 +487,6 @@ private:
 
     Scalar depthBOR_;
     Scalar injectionRate_;
-    Scalar eps_;
 
     int nTemperature_;
     int nPressure_;
diff --git a/test/porousmediumflow/co2/implicit/heterogeneousproblemni.hh b/test/porousmediumflow/co2/implicit/heterogeneousproblemni.hh
index 0dfefd9f0b339d51b89e5dde09302a3064fbb2da..dc7934dea2fc5a65ae9426302394ded8d6443bc5 100644
--- a/test/porousmediumflow/co2/implicit/heterogeneousproblemni.hh
+++ b/test/porousmediumflow/co2/implicit/heterogeneousproblemni.hh
@@ -196,8 +196,6 @@ public:
         // set the spatial parameters by reading the DGF grid file
         this->spatialParams().setParams();
 
-        eps_ = 1e-6;
-
         // initialize the tables of the fluid system
         FluidSystem::init(/*Tmin=*/temperatureLow_,
                           /*Tmax=*/temperatureHigh_,
@@ -508,7 +506,6 @@ private:
     Scalar injectionRate_;
     Scalar injectionPressure_;
     Scalar injectionTemperature_;
-    Scalar eps_;
 
     int nTemperature_;
     int nPressure_;
diff --git a/test/porousmediumflow/mpnc/implicit/combustionproblem1c.hh b/test/porousmediumflow/mpnc/implicit/combustionproblem1c.hh
index d133fbbbb45e3ad7949556df269c38c2b6af1771..c4c2f6d97067242333531227b54b6a81df5ab482 100644
--- a/test/porousmediumflow/mpnc/implicit/combustionproblem1c.hh
+++ b/test/porousmediumflow/mpnc/implicit/combustionproblem1c.hh
@@ -240,7 +240,6 @@ public:
 
     void init()
     {
-            eps_ = 1e-6;
             outputName_ = GET_RUNTIME_PARAM(TypeTag, std::string, Constants.outputName);
             nRestart_ = GET_RUNTIME_PARAM(TypeTag, int, Constants.nRestart);
             TInitial_ = GET_RUNTIME_PARAM(TypeTag, Scalar, InitialConditions.TInitial);
@@ -727,7 +726,7 @@ private:
     {   return globalPos[dimWorld-1] > this->bBoxMax()[dimWorld-1] - eps_;}
 
 private:
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;;
     int nTemperature_;
     int nPressure_;
     std::string outputName_;
diff --git a/test/porousmediumflow/mpnc/implicit/combustionspatialparams.hh b/test/porousmediumflow/mpnc/implicit/combustionspatialparams.hh
index abd2b36c477ecca41dc760b4f718e92e584bfd0a..2d329e34042c45a375ee5187db2b654c8219a17d 100644
--- a/test/porousmediumflow/mpnc/implicit/combustionspatialparams.hh
+++ b/test/porousmediumflow/mpnc/implicit/combustionspatialparams.hh
@@ -120,7 +120,6 @@ public:
     //! load parameters from input file and initialize parameter values
         void setInputInitialize()
         {
-                eps_                    = 1e-6;
                 // BEWARE! First the input values have to be set, then the material parameters can be set
 
                 // this is the parameter value from file part
@@ -335,8 +334,7 @@ public:
     }
 
 private:
-    Scalar eps_ ;
-
+    static constexpr Scalar eps_ = 1e-6;;
 
     // Porous Medium Domain
     Scalar intrinsicPermeability_ ;
diff --git a/test/porousmediumflow/mpnc/implicit/evaporationatmosphereproblem.hh b/test/porousmediumflow/mpnc/implicit/evaporationatmosphereproblem.hh
index 035541d7931dc26d8054583a4e84c7f611bb4369..8b71b3c1091877e841562727724c9e455b43008b 100644
--- a/test/porousmediumflow/mpnc/implicit/evaporationatmosphereproblem.hh
+++ b/test/porousmediumflow/mpnc/implicit/evaporationatmosphereproblem.hh
@@ -244,7 +244,6 @@ public:
 
     void init()
     {
-            eps_                    = 1e-6;
             percentOfEquil_         = GET_RUNTIME_PARAM(TypeTag, Scalar,BoundaryConditions.percentOfEquil);
             nTemperature_           = GET_RUNTIME_PARAM(TypeTag, int, FluidSystem.nTemperature);
             nPressure_              = GET_RUNTIME_PARAM(TypeTag, int, FluidSystem.nPressure);
@@ -745,7 +744,7 @@ private:
     {        return globalPos[dimWorld-1] > this->bBoxMax()[dimWorld-1] - eps_;    }
 
 private:
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;;
     Scalar percentOfEquil_ ;
     int nTemperature_;
     int nPressure_;
diff --git a/test/porousmediumflow/mpnc/implicit/evaporationatmospherespatialparams.hh b/test/porousmediumflow/mpnc/implicit/evaporationatmospherespatialparams.hh
index e76893389538885c5e18134bb76e52e25e706270..bf9c2ecc9e3fe2a96d65963432d3f62524e66988 100644
--- a/test/porousmediumflow/mpnc/implicit/evaporationatmospherespatialparams.hh
+++ b/test/porousmediumflow/mpnc/implicit/evaporationatmospherespatialparams.hh
@@ -198,7 +198,6 @@ public:
         // load parameters from input file and initialize parameter values
         void setInputInitialize()
         {
-                eps_                    = 1e-6;
                 heightPM_               = GET_RUNTIME_PARAM(TypeTag, Scalar, Grid.InterfacePosY);
                 heightDomain_           = GET_RUNTIME_PARAM(TypeTag, GlobalPosition, Grid.UpperRight)[1];
                 // BEWARE! First the input values have to be set, than the material parameters can be set
@@ -547,7 +546,7 @@ public:
      * -> be careful with neumannAtPos
      */
     bool inPM_(const GlobalPosition & globalPos) const
-    {       return ( (globalPos[dimWorld-1] > 0. - 1e-6) and (globalPos[dimWorld-1] < (heightPM_ + 1e-6 ) ) );   }
+    {       return ( (globalPos[dimWorld-1] > 0. - eps_) and (globalPos[dimWorld-1] < (heightPM_ + eps_) ) );   }
 
     /*!
      * \brief Give back whether the tested position (input) is a specific region (above PM / "free flow") in the domain
@@ -561,7 +560,7 @@ public:
      * -> be careful with neumannAtPos
      */
     bool inFF_(const GlobalPosition & globalPos) const
-    {       return ( (globalPos[dimWorld-1] < heightDomain_ + 1e-6) and (globalPos[dimWorld-1] > (heightPM_ + 1e-6) ) );   }
+    {       return ( (globalPos[dimWorld-1] < heightDomain_ + eps_) and (globalPos[dimWorld-1] > (heightPM_ + eps_) ) );   }
 
     /*!
      * \brief Give back whether the tested position (input) is a specific region (above PM / "free flow") in the domain
@@ -575,14 +574,14 @@ public:
      * -> be careful with neumannAtPos
      */
     bool inInjection_(const GlobalPosition & globalPos) const
-    {       return ( (globalPos[dimWorld-1] < heightDomain_ - 0.25*heightDomain_  + 1e-6) and (globalPos[dimWorld-1] > (heightPM_ + 1e-6) ) );   }
+    {       return ( (globalPos[dimWorld-1] < heightDomain_ - 0.25*heightDomain_  + eps_) and (globalPos[dimWorld-1] > (heightPM_ + eps_) ) );   }
 
     /*! \brief access function for the depth / height of the porous medium */
     const Scalar heightPM() const
     { return heightPM_; }
 
 private:
-    Scalar eps_ ;
+    static constexpr Scalar eps_  = 1e-6;;
     Scalar heightDomain_ ;
 
     AwnSurfaceParams    aWettingNonWettingSurfaceParams_;
diff --git a/test/porousmediumflow/mpnc/implicit/forchheimer1pproblem.hh b/test/porousmediumflow/mpnc/implicit/forchheimer1pproblem.hh
index 93f9357f6c92cc2b0c9f4fbdccc995069b9ec781..5fee54dbb0cd65f32b3ae6f552543e62d05daffe 100644
--- a/test/porousmediumflow/mpnc/implicit/forchheimer1pproblem.hh
+++ b/test/porousmediumflow/mpnc/implicit/forchheimer1pproblem.hh
@@ -157,7 +157,6 @@ public:
             pMin_ = GET_RUNTIME_PARAM(TypeTag, Scalar, Problem.pMin);
             outputName_     = GET_RUNTIME_PARAM(TypeTag, std::string, Problem.outputName);
 
-        eps_ = 1e-6;
         temperature_ = 273.15 + 25; // -> 25°C
 
         // initialize the tables of the fluid system
@@ -441,7 +440,7 @@ private:
     {        return globalPos[dimWorld-1] > this->bBoxMax()[dimWorld-1] - eps_;    }
 
     Scalar temperature_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;;
     std::string outputName_;
     Scalar pMax_, pMin_ ;
 
diff --git a/test/porousmediumflow/mpnc/implicit/forchheimer2pproblem.hh b/test/porousmediumflow/mpnc/implicit/forchheimer2pproblem.hh
index 0038bc413b63595fb885a51de80ccb01d94e2d7c..1262ed89ff76acebf3ef16671a113b8508503357 100644
--- a/test/porousmediumflow/mpnc/implicit/forchheimer2pproblem.hh
+++ b/test/porousmediumflow/mpnc/implicit/forchheimer2pproblem.hh
@@ -156,7 +156,6 @@ public:
             pMin_ = GET_RUNTIME_PARAM(TypeTag, Scalar, Problem.pMin);
             outputName_     = GET_RUNTIME_PARAM(TypeTag, std::string, Problem.outputName);
 
-        eps_ = 1e-6;
         temperature_ = 273.15 + 25; // -> 25°C
 
         // initialize the tables of the fluid system
@@ -435,7 +434,7 @@ private:
     {        return globalPos[0] > this->bBoxMax()[0] - eps_;    }
 
     Scalar temperature_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string outputName_;
     Scalar pMax_, pMin_ ;
 
diff --git a/test/porousmediumflow/mpnc/implicit/obstacleproblem.hh b/test/porousmediumflow/mpnc/implicit/obstacleproblem.hh
index 418dec999b43944f9e4467e02298c9086dfa9607..22a700abb7b116ce6dba918dce579404528352b7 100644
--- a/test/porousmediumflow/mpnc/implicit/obstacleproblem.hh
+++ b/test/porousmediumflow/mpnc/implicit/obstacleproblem.hh
@@ -155,7 +155,6 @@ public:
     ObstacleProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
     {
-        eps_ = 1e-6;
         temperature_ = 273.15 + 25; // -> 25°C
 
         // initialize the tables of the fluid system
@@ -429,18 +428,18 @@ private:
     {
         Scalar x = globalPos[0];
         Scalar y = globalPos[1];
-        return x >= 60 - eps_ && y <= 10;
+        return x >= 60 - eps_ && y <= 10 + eps_;
     }
 
     bool onOutlet_(const GlobalPosition &globalPos) const
     {
         Scalar x = globalPos[0];
         Scalar y = globalPos[1];
-        return x < eps_ && y <= 10;
+        return x < eps_ && y <= 10 + eps_;
     }
 
     Scalar temperature_;
-    Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
 };
 } //end namespace
diff --git a/test/porousmediumflow/mpnc/implicit/obstaclespatialparams.hh b/test/porousmediumflow/mpnc/implicit/obstaclespatialparams.hh
index ed4a1931275f93dba0991a154d05e31ff1e8a4bd..0f8b7580c2d08aaba999d695a1053e1c92821d75 100644
--- a/test/porousmediumflow/mpnc/implicit/obstaclespatialparams.hh
+++ b/test/porousmediumflow/mpnc/implicit/obstaclespatialparams.hh
@@ -182,8 +182,8 @@ private:
     static bool isFineMaterial_(const DimWorldVector &pos)
     {
         return
-            10 <= pos[0] && pos[0] <= 20 &&
-            0 <= pos[1] && pos[1] <= 35;
+            10 - eps_ <= pos[0] && pos[0] <= 20 + eps_ &&
+            0 - eps_ <= pos[1] && pos[1] <= 35 + eps_;
     }
 
     Scalar coarseK_;
@@ -191,6 +191,7 @@ private:
     Scalar porosity_;
     MaterialLawParams fineMaterialParams_;
     MaterialLawParams coarseMaterialParams_;
+    static constexpr Scalar eps_ = 1e-6;
 };
 
 }
diff --git a/test/porousmediumflow/richards/implicit/richardsanalyticalproblem.hh b/test/porousmediumflow/richards/implicit/richardsanalyticalproblem.hh
index c6f41fa4dba144618cbd36ceb02e64ce777339b8..41679a2c000bdb8b42c391afd9f1f62ca14d11d7 100644
--- a/test/porousmediumflow/richards/implicit/richardsanalyticalproblem.hh
+++ b/test/porousmediumflow/richards/implicit/richardsanalyticalproblem.hh
@@ -145,7 +145,6 @@ public:
                         const GridView &gridView)
         : ParentType(timeManager, gridView)
     {
-        eps_ = 3e-6;
         pnRef_ = 1e5; // air pressure
         name_ = GET_RUNTIME_PARAM_FROM_GROUP(TypeTag, std::string, Problem, Name);
     }
@@ -419,7 +418,7 @@ private:
         return globalPos[1] > this->bBoxMax()[1] - eps_;
     }
 
-    Scalar eps_;
+    static constexpr Scalar eps_ = 3e-6;
     Scalar pnRef_;
     std::string name_;
 };
diff --git a/test/porousmediumflow/richards/implicit/richardslensproblem.hh b/test/porousmediumflow/richards/implicit/richardslensproblem.hh
index be66fd45777b4c78d2a21ffdd2199320002b6649..acbef837da30b080264e1d5981b2080f7ead26e5 100644
--- a/test/porousmediumflow/richards/implicit/richardslensproblem.hh
+++ b/test/porousmediumflow/richards/implicit/richardslensproblem.hh
@@ -140,7 +140,6 @@ public:
                         const GridView &gridView)
         : ParentType(timeManager, gridView)
     {
-        eps_ = 3e-6;
         pnRef_ = 1e5;
 
         lensLowerLeft_[0] = 1.0;
@@ -335,7 +334,7 @@ private:
         return onUpperBoundary_(globalPos) && 0.5 < lambda && lambda < 2.0/3.0;
     }
 
-    Scalar eps_;
+    static constexpr Scalar eps_ = 3e-6;
     Scalar pnRef_;
 
     GlobalPosition lensLowerLeft_;
diff --git a/test/porousmediumflow/richards/implicit/richardslensspatialparams.hh b/test/porousmediumflow/richards/implicit/richardslensspatialparams.hh
index b518ed870f2d63c8969f749a7b27e41da70c1c03..46d85007cc1602b05947652a4a64413180006a83 100644
--- a/test/porousmediumflow/richards/implicit/richardslensspatialparams.hh
+++ b/test/porousmediumflow/richards/implicit/richardslensspatialparams.hh
@@ -194,7 +194,7 @@ private:
     bool isInLens_(const GlobalPosition &globalPos) const
     {
         for (int i = 0; i < dimWorld; ++i) {
-            if (globalPos[i] < lensLowerLeft_[i] || globalPos[i] > lensUpperRight_[i])
+            if (globalPos[i] < lensLowerLeft_[i] - eps_ || globalPos[i] > lensUpperRight_[i] + eps_)
                 return false;
         }
         return true;
@@ -207,6 +207,7 @@ private:
     Scalar outerK_;
     MaterialLawParams lensMaterialParams_;
     MaterialLawParams outerMaterialParams_;
+    static constexpr Scalar eps_ = 3e-6;
 };
 
 } // end namespace
diff --git a/test/porousmediumflow/richards/implicit/richardsniconductionproblem.hh b/test/porousmediumflow/richards/implicit/richardsniconductionproblem.hh
index 4d75c5aea5f786966ce0c41af3a2795d2278df6e..aa94b8250d6ff5d084a6084cb71956e9ee46fd78 100644
--- a/test/porousmediumflow/richards/implicit/richardsniconductionproblem.hh
+++ b/test/porousmediumflow/richards/implicit/richardsniconductionproblem.hh
@@ -130,7 +130,6 @@ class RichardsNIConductionProblem : public RichardsProblem<TypeTag>
 public:
     RichardsNIConductionProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-        , eps_(1e-6)
     {
         //initialize fluid system
         FluidSystem::init();
@@ -347,7 +346,7 @@ private:
     }
 
     Scalar temperatureHigh_;
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
     int outputInterval_;
 };
diff --git a/test/porousmediumflow/richards/implicit/richardsniconvectionproblem.hh b/test/porousmediumflow/richards/implicit/richardsniconvectionproblem.hh
index 7079debfad2decdd1bf1e67b2fc8d9064eb1294a..34e14263511edf227c28cea61e5c13e4017c1081 100644
--- a/test/porousmediumflow/richards/implicit/richardsniconvectionproblem.hh
+++ b/test/porousmediumflow/richards/implicit/richardsniconvectionproblem.hh
@@ -135,7 +135,6 @@ class RichardsNIConvectionProblem : public RichardsProblem<TypeTag>
 public:
     RichardsNIConvectionProblem(TimeManager &timeManager, const GridView &gridView)
         : ParentType(timeManager, gridView)
-        , eps_(1e-6)
     {
         //initialize fluid system
         FluidSystem::init();
@@ -380,7 +379,7 @@ private:
     Scalar pressureHigh_;
     Scalar pressureLow_;
     Scalar darcyVelocity_;
-    const Scalar eps_;
+    static constexpr Scalar eps_ = 1e-6;
     std::string name_;
     int outputInterval_;
 };