diff --git a/dumux/discretization/CMakeLists.txt b/dumux/discretization/CMakeLists.txt
index d67d77fbf4c4001da671f855413882ec8399d3f7..812b30de3f33e870c69381002771eca417e2ab0b 100644
--- a/dumux/discretization/CMakeLists.txt
+++ b/dumux/discretization/CMakeLists.txt
@@ -2,6 +2,7 @@ add_subdirectory(box)
 add_subdirectory(cellcentered)
 add_subdirectory(fem)
 add_subdirectory(staggered)
+add_subdirectory(projection)
 
 install(FILES
 basefvgridgeometry.hh
@@ -13,6 +14,7 @@ elementsolution.hh
 evalgradients.hh
 evalsolution.hh
 fluxstencil.hh
+functionspacebasis.hh
 fvgridvariables.hh
 fvproperties.hh
 localview.hh
diff --git a/dumux/discretization/functionspacebasis.hh b/dumux/discretization/functionspacebasis.hh
new file mode 100644
index 0000000000000000000000000000000000000000..ec371baecfaed0fd9052b2d531459c23b31cd13d
--- /dev/null
+++ b/dumux/discretization/functionspacebasis.hh
@@ -0,0 +1,94 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ *   See the file COPYING for full copying permissions.                      *
+ *                                                                           *
+ *   This program is free software: you can redistribute it and/or modify    *
+ *   it under the terms of the GNU General Public License as published by    *
+ *   the Free Software Foundation, either version 3 of the License, or       *
+ *   (at your option) any later version.                                     *
+ *                                                                           *
+ *   This program is distributed in the hope that it will be useful,         *
+ *   but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+ *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the            *
+ *   GNU General Public License for more details.                            *
+ *                                                                           *
+ *   You should have received a copy of the GNU General Public License       *
+ *   along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup Discretization
+ * \brief Provides helper aliases and functionality to obtain the types
+ *        and instances of Dune::Functions function space bases that
+ *        underlie different discretization schemes
+ */
+#ifndef DUMUX_DISCRETIZATION_FUNCTION_SPACE_BASIS_HH
+#define DUMUX_DISCRETIZATION_FUNCTION_SPACE_BASIS_HH
+
+#if HAVE_DUNE_FUNCTIONS
+
+#include <dumux/discretization/method.hh>
+#include <dune/functions/functionspacebases/lagrangebasis.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup Discretization
+ * \brief Traits class that contains information on the
+ *        function space basis used by the discretization
+ *        scheme underlying a grid geometry class. Specializations
+ *        of the traits for different schemes are provided below.
+ */
+template< class GridGeometry,
+          DiscretizationMethod dm = GridGeometry::discMethod >
+struct FunctionSpaceBasisTraits;
+
+/*!
+ * \ingroup Discretization
+ * \brief Creates a Dune::Functions object of the underlying basis
+ *        of a discretization scheme that is not finite elements.
+ */
+template<class GridGeometry, std::enable_if_t<GridGeometry::discMethod != DiscretizationMethod::fem, int> = 0>
+typename FunctionSpaceBasisTraits<GridGeometry>::GlobalBasis
+getFunctionSpaceBasis(const GridGeometry& gridGeometry)
+{ return {gridGeometry.gridView()}; }
+
+/*!
+ * \ingroup Discretization
+ * \brief Returns the Dune::Functions object for the basis of a finite element scheme.
+ */
+template<class GridGeometry, std::enable_if_t<GridGeometry::discMethod == DiscretizationMethod::fem, int> = 0>
+const typename FunctionSpaceBasisTraits<GridGeometry>::GlobalBasis&
+getFunctionSpaceBasis(const GridGeometry& gridGeometry)
+{ return gridGeometry.feBasis(); }
+
+
+///////////////////////////////////////////////////////////
+// Specializations of the FunctionSpaceBasisTraits class //
+///////////////////////////////////////////////////////////
+
+//! Traits specialization: box scheme uses lagrange basis of order 1
+template< class GridGeometry >
+struct FunctionSpaceBasisTraits<GridGeometry, DiscretizationMethod::box>
+{ using GlobalBasis = Dune::Functions::LagrangeBasis<typename GridGeometry::GridView, /*order*/1>; };
+
+//! Traits specialization: cc schemes use lagrange bases of order 0
+template< class GridGeometry >
+struct FunctionSpaceBasisTraits<GridGeometry, DiscretizationMethod::cctpfa>
+{ using GlobalBasis = Dune::Functions::LagrangeBasis<typename GridGeometry::GridView, /*order*/0>; };
+
+//! Traits specialization: cc schemes use lagrange bases of order 0
+template< class GridGeometry >
+struct FunctionSpaceBasisTraits<GridGeometry, DiscretizationMethod::ccmpfa>
+{ using GlobalBasis = Dune::Functions::LagrangeBasis<typename GridGeometry::GridView, /*order*/0>; };
+
+//! Traits specialization: fem defines its basis
+template< class GridGeometry >
+struct FunctionSpaceBasisTraits<GridGeometry, DiscretizationMethod::fem>
+{ using GlobalBasis = typename GridGeometry::FEBasis; };
+
+} // end namespace Dumux
+
+#endif // HAVE_DUNE_FUNCTIONS
+#endif // DUMUX_FUNCTION_SPACE_BASIS_HH
diff --git a/dumux/discretization/projection/CMakeLists.txt b/dumux/discretization/projection/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f3f288c353f6a972f27fa5cb6c41534674bb9ff0
--- /dev/null
+++ b/dumux/discretization/projection/CMakeLists.txt
@@ -0,0 +1,3 @@
+install(FILES
+projector.hh
+DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dumux/discretization/projection)
diff --git a/dumux/discretization/projection/projector.hh b/dumux/discretization/projection/projector.hh
new file mode 100644
index 0000000000000000000000000000000000000000..a4a3824d97dcebcfac072fbe81530c8cd2be5c5a
--- /dev/null
+++ b/dumux/discretization/projection/projector.hh
@@ -0,0 +1,342 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ *   See the file COPYING for full copying permissions.                      *
+ *                                                                           *
+ *   This program is free software: you can redistribute it and/or modify    *
+ *   it under the terms of the GNU General Public License as published by    *
+ *   the Free Software Foundation, either version 3 of the License, or       *
+ *   (at your option) any later version.                                     *
+ *                                                                           *
+ *   This program is distributed in the hope that it will be useful,         *
+ *   but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+ *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the            *
+ *   GNU General Public License for more details.                            *
+ *                                                                           *
+ *   You should have received a copy of the GNU General Public License       *
+ *   along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+ *****************************************************************************/
+/*!
+ * \file
+ * \ingroup Discretization
+ * \brief Contains functionality for L2-projections from one function
+ *        space into another, which can live both on the same or different
+ *        grids of potentially different dimensionality.
+ * \note In the case of the function space bases living on the same grid
+ *       an optimized implementation could be implemented. Currently, we
+ *       require a glue object containing the intersections between two
+ *       grids to be provided to the free factory functions.
+ */
+#ifndef DUMUX_DISCRETIZATION_PROJECTOR_HH
+#define DUMUX_DISCRETIZATION_PROJECTOR_HH
+
+#include <string>
+#include <utility>
+#include <type_traits>
+
+#include <dune/common/timer.hh>
+#include <dune/common/fmatrix.hh>
+#include <dune/common/exceptions.hh>
+#include <dune/common/promotiontraits.hh>
+
+#include <dune/geometry/quadraturerules.hh>
+#include <dune/istl/matrixindexset.hh>
+
+#include <dumux/common/parameters.hh>
+#include <dumux/linear/seqsolverbackend.hh>
+#include <dumux/assembly/jacobianpattern.hh>
+#include <dumux/discretization/functionspacebasis.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup Discretization
+ * \brief Does an L2-projection from one discrete function space
+ *        into another. The convenience functions makeProjectorPair
+ *        or makeProjector can be used to create such a projection.
+ */
+template<class Scalar>
+class Projector
+{
+    using BlockType = Dune::FieldMatrix<Scalar, 1, 1>;
+
+public:
+    //! Export the type of the projection matrices
+    using Matrix = Dune::BCRSMatrix< BlockType >;
+
+    //! delete default constructor
+    Projector() = delete;
+
+    /*!
+     * \brief Constructor. Receives the mass and projection
+     *        matrix that define the linear system describing
+     *        the L2-projection from a function space into another.
+     */
+    Projector(Matrix&& massMatrix, Matrix&& projectionMatrix)
+    : massMat_(std::move(massMatrix))
+    , projMat_(std::move(projectionMatrix))
+    {}
+
+    /*!
+     * \brief Project a solution u into up
+     * \param u The solution living on the domain space
+     * \param up The projection of u into the target space
+     */
+    template< class DomainSolution, class TargetSolution>
+    void project(const DomainSolution& u, TargetSolution& up) const
+    {
+        // be picky about size of u
+        if ( u.size() != projMat_.M())
+            DUNE_THROW(Dune::InvalidStateException, "Vector size mismatch" );
+
+        up.resize(massMat_.N());
+
+        auto rhs = up;
+        projMat_.mv(u, rhs);
+
+        SSORCGBackend solver;
+        solver.solve(massMat_, up, rhs);
+    }
+
+private:
+    Matrix massMat_;
+    Matrix projMat_;
+};
+
+/*!
+ * \brief Traits class stating the type of projector between to bases
+ */
+template<class FEBasisDomain, class FEBasisTarget>
+class ProjectorTraits
+{
+    using FiniteElementDomain = typename FEBasisDomain::LocalView::Tree::FiniteElement;
+    using FiniteElementTarget = typename FEBasisTarget::LocalView::Tree::FiniteElement;
+    using ScalarDomain = typename FiniteElementDomain::Traits::LocalBasisType::Traits::RangeFieldType;
+    using ScalarTarget = typename FiniteElementTarget::Traits::LocalBasisType::Traits::RangeFieldType;
+    using Scalar = typename Dune::PromotionTraits<ScalarDomain, ScalarTarget>::PromotedType;
+public:
+    using Projector = Dumux::Projector< Scalar >;
+};
+
+
+// Projector construction details
+namespace Impl {
+
+/*!
+ * \brief Creates a projector class between two function space bases
+ * \tparam doBidirectional If false, the backward projection matrix is not assembled
+ */
+template<bool doBidirectional, class FEBasisDomain, class FEBasisTarget, class GlueType>
+std::pair< typename ProjectorTraits<FEBasisDomain, FEBasisTarget>::Projector,
+           typename ProjectorTraits<FEBasisTarget, FEBasisDomain>::Projector >
+makeProjectorPair(const FEBasisDomain& feBasisDomain,
+                  const FEBasisTarget& feBasisTarget,
+                  const GlueType& glue)
+{
+    // we assume that target dim <= domain dimension
+    static constexpr int domainDim = FEBasisDomain::GridView::dimension;
+    static constexpr int targetDim = FEBasisTarget::GridView::dimension;
+    static_assert(targetDim <= domainDim, "This expects target dim < domain dim, please swap arguments");
+
+    using ForwardProjector = typename ProjectorTraits<FEBasisDomain, FEBasisTarget>::Projector;
+    using BackwardProjector = typename ProjectorTraits<FEBasisTarget, FEBasisDomain>::Projector;
+
+    using ForwardProjectionMatrix = typename ForwardProjector::Matrix;
+    using BackwardProjectionMatrix = typename BackwardProjector::Matrix;
+
+    auto domainLocalView = feBasisDomain.localView();
+    auto targetLocalView = feBasisTarget.localView();
+
+    // determine mass matrix patterns (standard FE scheme pattern)
+    Dune::MatrixIndexSet backwardPatternM, forwardPatternM;
+    forwardPatternM = getFEJacobianPattern(feBasisTarget);
+    if (doBidirectional) backwardPatternM = getFEJacobianPattern(feBasisDomain);
+
+    // determine projection matrix patterns
+    Dune::MatrixIndexSet backwardPatternP, forwardPatternP;
+    forwardPatternP.resize(feBasisTarget.size(), feBasisDomain.size());
+    if (doBidirectional) backwardPatternP.resize(feBasisDomain.size(), feBasisTarget.size());
+
+    using std::max;
+    unsigned int maxBasisOrder = 0;
+    for (const auto& is : intersections(glue))
+    {
+        // "outside" element is of target domain
+        // since target dim <= domain dim there is maximum one!
+        targetLocalView.bind( is.outside(0) );
+        const auto& targetLocalBasis = targetLocalView.tree().finiteElement().localBasis();
+
+        for (unsigned int nIdx = 0; nIdx < is.neighbor(/*targetSide*/1); ++nIdx)
+        {
+            domainLocalView.bind( is.inside(nIdx) );
+            const auto& domainLocalBasis = domainLocalView.tree().finiteElement().localBasis();
+
+            // keep track of maximum basis order (used in integration)
+            maxBasisOrder = max(maxBasisOrder, max(domainLocalBasis.order(), targetLocalBasis.order()));
+
+            for (unsigned int i = 0; i < domainLocalBasis.size(); ++i)
+                for (unsigned int j = 0; j < targetLocalBasis.size(); ++j)
+                {
+                    forwardPatternP.add(targetLocalView.index(j), domainLocalView.index(i));
+                    if (doBidirectional) backwardPatternP.add(domainLocalView.index(i), targetLocalView.index(j));
+                }
+        }
+    }
+
+    // assemble matrices
+    ForwardProjectionMatrix forwardM, forwardP;
+    forwardPatternM.exportIdx(forwardM); forwardM = 0.0;
+    forwardPatternP.exportIdx(forwardP); forwardP = 0.0;
+
+    BackwardProjectionMatrix backwardM, backwardP;
+    if (doBidirectional)
+    {
+        backwardPatternM.exportIdx(backwardM); backwardM = 0.0;
+        backwardPatternP.exportIdx(backwardP); backwardP = 0.0;
+    }
+
+    for (const auto& is : intersections(glue))
+    {
+        const auto& targetElement = is.outside(0);
+        const auto& targetElementGeometry = targetElement.geometry();
+
+        targetLocalView.bind( targetElement );
+        const auto& targetLocalBasis = targetLocalView.tree().finiteElement().localBasis();
+
+        // perform integration over intersection geometry
+        using IsGeometry = typename std::decay_t<decltype(is.geometry())>;
+        using ctype = typename IsGeometry::ctype;
+
+        const auto& isGeometry = is.geometry();
+        const int intOrder = maxBasisOrder + 1;
+        const auto& quad = Dune::QuadratureRules<ctype, IsGeometry::mydimension>::rule(isGeometry.type(), intOrder);
+        for (auto&& qp : quad)
+        {
+            const auto weight = qp.weight();
+            const auto ie = isGeometry.integrationElement(qp.position());
+            const auto globalPos = isGeometry.global(qp.position());
+
+            std::vector< Dune::FieldVector<ctype, 1> > targetShapeVals;
+            targetLocalBasis.evaluateFunction(targetElementGeometry.local(globalPos), targetShapeVals);
+
+            // mass matrix entries target domain
+            for (unsigned int i = 0; i < targetLocalBasis.size(); ++i)
+            {
+                const auto dofIdx = targetLocalView.index(i);
+                forwardM[dofIdx][dofIdx] += ie*weight*targetShapeVals[i];
+            }
+
+            // If targetDim < domainDim, there can be several "neighbors" if
+            // targetElement is aligned with a facet of domainElement. In
+            // this case make sure the basis functions are not added
+            // multiple times! (division by numNeighbors)
+            const auto numNeighbors = is.neighbor(/*targetSide*/1);
+            for (unsigned int nIdx = 0; nIdx < numNeighbors; ++nIdx)
+            {
+                const auto& domainElement = is.inside(nIdx);
+                domainLocalView.bind( domainElement );
+                const auto& domainLocalBasis = domainLocalView.tree().finiteElement().localBasis();
+
+                std::vector< Dune::FieldVector<ctype, 1> > domainShapeVals;
+                domainLocalBasis.evaluateFunction(domainElement.geometry().local(globalPos), domainShapeVals);
+
+                // add entries in matrices
+                for (unsigned int i = 0; i < domainLocalBasis.size(); ++i)
+                {
+                    const auto dofIdxDomain = domainLocalView.index(i);
+                    const auto domainShapeVal = domainShapeVals[i];
+                    backwardM[dofIdxDomain][dofIdxDomain] += ie*weight*domainShapeVal;
+
+                    for (unsigned int j = 0; j < targetLocalBasis.size(); ++j)
+                    {
+                        const auto dofIdxTarget = targetLocalView.index(j);
+                        const auto entry = ie*weight*domainShapeVal*targetShapeVals[j];
+
+                        forwardP[dofIdxTarget][dofIdxDomain] += entry/numNeighbors;
+                        if (doBidirectional)
+                            backwardP[dofIdxDomain][dofIdxTarget] += entry;
+                    }
+                }
+            }
+        }
+    }
+
+    // On those dofs that to not take part in any intersection we will have zeroes
+    // in the mass matrices. The right hand side will be zero because the projection
+    // matrix has no entries for those dofs as there was no intersection. Thus, we set
+    // 1.0 on the diagonal for those dofs, such that after projection, the projected
+    // solution is 0 on them.
+    for (std::size_t dofIdx = 0; dofIdx < forwardM.N(); ++dofIdx)
+        if (forwardM[dofIdx][dofIdx] == 0.0)
+            forwardM[dofIdx][dofIdx] = 1.0;
+
+    if (doBidirectional)
+    {
+        for (std::size_t dofIdx = 0; dofIdx < backwardM.N(); ++dofIdx)
+            if (backwardM[dofIdx][dofIdx] == 0.0)
+                backwardM[dofIdx][dofIdx] = 1.0;
+    }
+
+    ForwardProjector fw(std::move(forwardM), std::move(forwardP));
+    BackwardProjector bw(std::move(backwardM), std::move(backwardP));
+
+    return std::make_pair(std::move(fw), std::move(bw));
+}
+
+} // end namespace Implementation
+
+
+/*!
+ * \ingroup Discretization
+ * \brief Creates a pair of projectors between the space with
+ *        basis feBasisDomain to the space with basis feBasisTarget.
+ * \param feBasisDomain The domain finite element space basis
+ * \param feBasisTarget The target finite element space basis
+ * \param glue The glue object containing the intersections between the grids.
+ * \return A pair of projectors where the first is the forward
+ *         projector from the space with basis feBasisDomain to
+ *         the space with basis feBasisTarget and the second
+ *         does the backward projection.
+ */
+template< class FEBasisDomain, class FEBasisTarget, class GlueType >
+std::pair< typename ProjectorTraits<FEBasisDomain, FEBasisTarget>::Projector,
+           typename ProjectorTraits<FEBasisTarget, FEBasisDomain>::Projector >
+makeProjectorPair(const FEBasisDomain& feBasisDomain,
+                  const FEBasisTarget& feBasisTarget,
+                  GlueType glue)
+{
+    // we assume that target dim <= domain dimension
+    static constexpr int domainDim = FEBasisDomain::GridView::dimension;
+    static constexpr int targetDim = FEBasisTarget::GridView::dimension;
+    static_assert(targetDim <= domainDim, "makeProjectorPair() expects targetDim < domainDim, please swap arguments");
+
+    return Impl::makeProjectorPair<true>(feBasisDomain, feBasisTarget, glue);
+}
+
+/*!
+ * \ingroup Discretization
+ * \brief Creates a forward projector from the space feBasisDomain
+ *        to the space with basis feBasisTarget.
+ * \param feBasisDomain The domain finite element space basis
+ * \param feBasisTarget The target finite element space basis
+ * \param glue The glue object containing the intersections between the grids.
+ * \return The forward projector from the space with basis feBasisDomain
+ *         to the space with basis feBasisTarget.
+ */
+template< class FEBasisDomain, class FEBasisTarget, class GlueType >
+typename ProjectorTraits<FEBasisDomain, FEBasisTarget>::Projector
+makeProjector(const FEBasisDomain& feBasisDomain,
+              const FEBasisTarget& feBasisTarget,
+              GlueType glue)
+{
+    // we assume that target dim <= domain dimension
+    static constexpr int domainDim = FEBasisDomain::GridView::dimension;
+    static constexpr int targetDim = FEBasisTarget::GridView::dimension;
+    static_assert(targetDim <= domainDim, "makeProjectorPair() expects targetDim < domainDim, please swap arguments");
+
+    return Impl::makeProjectorPair<false>(feBasisDomain, feBasisTarget, glue).first;
+}
+
+} // end namespace Dumux
+
+#endif // DUMUX_PROJECTOR_HH
diff --git a/dune.module b/dune.module
index 5635a5a85c9ab861b7ca5a300009fb4caedccb71..261fdfcf42a8a0c4089c4a027021c75c520ebe50 100644
--- a/dune.module
+++ b/dune.module
@@ -2,5 +2,5 @@ Module: dumux
 Version: 3.1-git
 Maintainer: dumux@listserv.uni-stuttgart.de
 Depends: dune-common (>= 2.6) dune-grid (>= 2.6) dune-localfunctions (>= 2.6) dune-istl (>= 2.6)
-Suggests: dune-alugrid (>=2.6) dune-foamgrid (>=2.6) dune-uggrid (>=2.6) opm-common opm-grid dune-subgrid dune-spgrid (>= 2.6)
+Suggests: dune-alugrid (>=2.6) dune-foamgrid (>=2.6) dune-uggrid (>=2.6) dune-functions (>=2.6) opm-common opm-grid dune-subgrid dune-spgrid (>= 2.6)
 Whitespace-Hook: Yes
diff --git a/test/discretization/CMakeLists.txt b/test/discretization/CMakeLists.txt
index b42b74522ab08268f20e2097f3e1509b9984e348..f127b603f79c94575badc24a7eb39c9328c88892 100644
--- a/test/discretization/CMakeLists.txt
+++ b/test/discretization/CMakeLists.txt
@@ -1,3 +1,4 @@
 add_subdirectory(cellcentered)
 add_subdirectory(staggered)
 add_subdirectory(box)
+add_subdirectory(projection)
diff --git a/test/discretization/projection/CMakeLists.txt b/test/discretization/projection/CMakeLists.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cec331a494c782e4a9771ebb3e54fccb4021c1ab
--- /dev/null
+++ b/test/discretization/projection/CMakeLists.txt
@@ -0,0 +1,41 @@
+dune_symlink_to_source_files(FILES "params.input")
+
+dune_add_test(NAME test_projection_2d1d
+              SOURCES test_projection_2d1d.cc
+              CMAKE_GUARD "( dune-foamgrid_FOUND AND dune-functions_FOUND )"
+              LABELS unit discretization
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              CMD_ARGS  --script fuzzyData
+                        --files ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_tpfa_tpfa_1d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/1d_tpfa_tpfa.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_tpfa_tpfa_2d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/2d_tpfa_tpfa.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_box_box_1d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/1d_box_box.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_box_box_2d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/2d_box_box.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_fem_fem_1d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/1d_fem_fem.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_fem_fem_2d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/2d_fem_fem.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_tpfa_box_1d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/1d_tpfa_box.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_tpfa_box_2d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/2d_tpfa_box.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_box_tpfa_1d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/1d_box_tpfa.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_box_tpfa_2d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/2d_box_tpfa.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_fem_box_2d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/2d_fem_box.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_fem_box_1d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/1d_fem_box.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_fem_tpfa_2d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/2d_fem_tpfa.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_fem_tpfa_1d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/1d_fem_tpfa.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_tpfa_fem_2d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/2d_tpfa_fem.csv
+                                ${CMAKE_SOURCE_DIR}/test/references/test_projection_2d1d_tpfa_fem_1d.csv
+                                ${CMAKE_CURRENT_BINARY_DIR}/1d_tpfa_fem.csv
+                       --command "${CMAKE_CURRENT_BINARY_DIR}/test_projection_2d1d params.input")
diff --git a/test/discretization/projection/params.input b/test/discretization/projection/params.input
new file mode 100644
index 0000000000000000000000000000000000000000..5058750258c5ce67e703e5ff8c0e9427aeb52004
--- /dev/null
+++ b/test/discretization/projection/params.input
@@ -0,0 +1,2 @@
+[Vtk]
+EnableOutput = false
diff --git a/test/discretization/projection/test_projection_2d1d.cc b/test/discretization/projection/test_projection_2d1d.cc
new file mode 100644
index 0000000000000000000000000000000000000000..16dd7b00387710a8d04b6d047fc5f54406f6463e
--- /dev/null
+++ b/test/discretization/projection/test_projection_2d1d.cc
@@ -0,0 +1,215 @@
+// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
+// vi: set et ts=4 sw=4 sts=4:
+/*****************************************************************************
+ *   See the file COPYING for full copying permissions.                      *
+ *                                                                           *
+ *   This program is free software: you can redistribute it and/or modify    *
+ *   it under the terms of the GNU General Public License as published by    *
+ *   the Free Software Foundation, either version 3 of the License, or       *
+ *   (at your option) any later version.                                     *
+ *                                                                           *
+ *   This program is distributed in the hope that it will be useful,         *
+ *   but WITHOUT ANY WARRANTY; without even the implied warranty of          *
+ *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the            *
+ *   GNU General Public License for more details.                            *
+ *                                                                           *
+ *   You should have received a copy of the GNU General Public License       *
+ *   along with this program.  If not, see <http://www.gnu.org/licenses/>.   *
+ *****************************************************************************/
+/*!
+ * \file
+ * \brief Test for the projection of discrete solutions from
+ *        a two-dimensional discrete solution to a one-dimensional.
+ */
+#include <config.h>
+
+#include <iostream>
+#include <fstream>
+#include <cmath>
+
+#include <dune/common/fvector.hh>
+#include <dune/istl/bvector.hh>
+
+#include <dune/grid/utility/structuredgridfactory.hh>
+#include <dune/grid/io/file/vtk/vtkwriter.hh>
+#include <dune/grid/yaspgrid.hh>
+#include <dune/foamgrid/foamgrid.hh>
+
+#include <dune/functions/functionspacebases/lagrangebasis.hh>
+#include <dune/functions/functionspacebases/interpolate.hh>
+#include <dune/functions/gridfunctions/discreteglobalbasisfunction.hh>
+
+#include <dumux/io/container.hh>
+#include <dumux/common/parameters.hh>
+
+#include <dumux/discretization/box/fvgridgeometry.hh>
+#include <dumux/discretization/fem/fegridgeometry.hh>
+#include <dumux/discretization/cellcentered/tpfa/fvgridgeometry.hh>
+#include <dumux/discretization/projection/projector.hh>
+#include <dumux/multidomain/glue.hh>
+
+template< class Scalar, class SolutionVector, class GridGeometry1, class GridGeometry2 >
+void writeProjection(const GridGeometry1& gg1, const GridGeometry2& gg2,
+                     const SolutionVector& sol1, const SolutionVector& sol2,
+                     const std::string& acro1, const std::string& acro2)
+{
+    const auto projectors = Dumux::makeProjectorPair( getFunctionSpaceBasis(gg1),
+                                                      getFunctionSpaceBasis(gg2),
+                                                      makeGlue(gg1, gg2) );
+    const auto& forwardProjector = projectors.first;
+    const auto& backwardProjector = projectors.second;
+
+    SolutionVector p2_1, p1_2;
+    forwardProjector.project(sol1, p2_1);
+    backwardProjector.project(sol2, p1_2);
+
+    const std::string filename1 = "2d_" + acro1 + "_" + acro2;
+    const std::string filename2 = "1d_" + acro1 + "_" + acro2;
+
+    Dumux::writeContainerToFile(p1_2, filename1 + ".csv");
+    Dumux::writeContainerToFile(p2_1, filename2 + ".csv");
+
+    static const bool writeVtk = Dumux::getParam<bool>("Vtk.EnableOutput", false);
+    if (writeVtk)
+    {
+        using namespace Dune;
+        VTKWriter<typename GridGeometry1::GridView> writer1(gg1.gridView());
+        VTKWriter<typename GridGeometry2::GridView> writer2(gg2.gridView());
+
+        const auto& basis1 = Dumux::getFunctionSpaceBasis(gg1);
+        const auto& basis2 = Dumux::getFunctionSpaceBasis(gg2);
+
+        const auto uInfo = VTK::FieldInfo("u", VTK::FieldInfo::Type::scalar, 1);
+        const auto upInfo = VTK::FieldInfo("u_p", VTK::FieldInfo::Type::scalar, 1);
+
+        const auto uFunction1 = Functions::makeDiscreteGlobalBasisFunction<Scalar>(basis1, sol1);
+        const auto uFunction2 = Functions::makeDiscreteGlobalBasisFunction<Scalar>(basis2, sol2);
+        const auto upFunction1 = Functions::makeDiscreteGlobalBasisFunction<Scalar>(basis1, p1_2);
+        const auto upFunction2 = Functions::makeDiscreteGlobalBasisFunction<Scalar>(basis2, p2_1);
+
+        if (GridGeometry1::discMethod == Dumux::DiscretizationMethod::cctpfa)
+        {
+            writer1.addCellData(uFunction1, uInfo);
+            writer1.addCellData(upFunction1, upInfo);
+        }
+        else
+        {
+            writer1.addVertexData(uFunction1, uInfo);
+            writer1.addVertexData(upFunction1, upInfo);
+        }
+
+        if (GridGeometry2::discMethod == Dumux::DiscretizationMethod::cctpfa)
+        {
+            writer2.addCellData(uFunction2, uInfo);
+            writer2.addCellData(upFunction2, upInfo);
+        }
+        else
+        {
+            writer2.addVertexData(uFunction2, uInfo);
+            writer2.addVertexData(upFunction2, upInfo);
+        }
+
+        writer1.write(filename1);
+        writer2.write(filename2);
+    }
+}
+
+int main (int argc, char *argv[]) try
+{
+    // maybe initialize mpi
+    Dune::MPIHelper::instance(argc, argv);
+
+    // initialize parameter tree
+    Dumux::Parameters::init(argc, argv);
+
+    using Grid1 = Dune::YaspGrid<2>;
+    using Grid2 = Dune::FoamGrid<1, 2>;
+
+    using GridView1 = typename Grid1::LeafGridView;
+    using GridView2 = typename Grid2::LeafGridView;
+    using FEBasis1 = Dune::Functions::LagrangeBasis<GridView1, 1>;
+    using FEBasis2 = Dune::Functions::LagrangeBasis<GridView2, 1>;
+
+    using Scalar = double;
+    using TpfaGridGeometry1 = Dumux::CCTpfaFVGridGeometry<GridView1>;
+    using BoxGridGeometry1 = Dumux::BoxFVGridGeometry<Scalar, GridView1>;
+    using FEGridGeometry1 = Dumux::FEGridGeometry<FEBasis1>;
+
+    using TpfaGridGeometry2 = Dumux::CCTpfaFVGridGeometry<GridView2>;
+    using BoxGridGeometry2 = Dumux::BoxFVGridGeometry<Scalar, GridView2>;
+    using FEGridGeometry2 = Dumux::FEGridGeometry<FEBasis2>;
+
+    // make the 2d grid
+    using GlobalPosition = Dune::FieldVector<Scalar, 2>;
+    GlobalPosition lower1(0.0);
+    GlobalPosition upper1(1.0);
+    std::array<unsigned int, 2> els1{{10, 10}};
+    std::shared_ptr<Grid1> grid1 = Dune::StructuredGridFactory<Grid1>::createCubeGrid(lower1, upper1, els1);
+
+    // make the 1d grid
+    GlobalPosition lower2({0., 0.5});
+    GlobalPosition upper2({1. ,0.5});
+    std::array<unsigned int, 1> els2{{13}};
+    std::shared_ptr<Grid2> grid2 = Dune::StructuredGridFactory<Grid2>::createSimplexGrid(lower2, upper2, els2);
+
+    Dune::Functions::LagrangeBasis<GridView1, 0> q0Basis1(grid1->leafGridView());
+    Dune::Functions::LagrangeBasis<GridView2, 0> q0Basis2(grid2->leafGridView());
+    Dune::Functions::LagrangeBasis<GridView1, 1> q1Basis1(grid1->leafGridView());
+    Dune::Functions::LagrangeBasis<GridView2, 1> q1Basis2(grid2->leafGridView());
+
+    // create all grid geometries
+    TpfaGridGeometry1 tpfaGridGeometry1(grid1->leafGridView());
+    BoxGridGeometry1 boxGridGeometry1(grid1->leafGridView());
+    FEGridGeometry1 feGridGeometry1(std::make_shared<FEBasis1>(grid1->leafGridView()));
+
+    TpfaGridGeometry2 tpfaGridGeometry2(grid2->leafGridView());
+    BoxGridGeometry2 boxGridGeometry2(grid2->leafGridView());
+    FEGridGeometry2 feGridGeometry2(std::make_shared<FEBasis2>(grid2->leafGridView()));
+
+    // function to distribute on grids
+    auto evalFunction1 = [] (const auto& pos)
+    { return std::sin(2*M_PI*pos[0])*std::cos(4*M_PI*pos[1]); };
+    auto evalFunction2 = [] (const auto& pos)
+    { return std::cos(4*M_PI*(pos[0] - M_PI))*std::sin(2*M_PI*(pos[1]-M_PI/2.0)); };
+
+    // create solution vectors
+    using SolutionVector = Dune::BlockVector< Dune::FieldVector<Scalar, 1> >;
+    SolutionVector sol2d_tpfa, sol2d_box, sol2d_fem;
+    SolutionVector sol1d_tpfa, sol1d_box, sol1d_fem;
+
+    Dune::Functions::interpolate(q0Basis1, sol2d_tpfa, evalFunction1);
+    Dune::Functions::interpolate(q0Basis2, sol1d_tpfa, evalFunction2);
+
+    Dune::Functions::interpolate(q1Basis1, sol2d_box, evalFunction1);
+    Dune::Functions::interpolate(q1Basis2, sol1d_box, evalFunction2);
+
+    Dune::Functions::interpolate(feGridGeometry1.feBasis(), sol2d_fem, evalFunction1);
+    Dune::Functions::interpolate(feGridGeometry2.feBasis(), sol1d_fem, evalFunction2);
+
+    // tpfa - tpfa
+    writeProjection<Scalar>(tpfaGridGeometry1, tpfaGridGeometry2, sol2d_tpfa, sol1d_tpfa, "tpfa", "tpfa");
+    // box - box
+    writeProjection<Scalar>(boxGridGeometry1, boxGridGeometry2, sol2d_box, sol1d_box, "box", "box");
+    // fem - fem
+    writeProjection<Scalar>(feGridGeometry1, feGridGeometry2, sol2d_fem, sol1d_fem, "fem", "fem");
+    // box - tpfa
+    writeProjection<Scalar>(boxGridGeometry1, tpfaGridGeometry2, sol2d_box, sol1d_tpfa, "box", "tpfa");
+    // tpfa - box
+    writeProjection<Scalar>(tpfaGridGeometry1, boxGridGeometry2, sol2d_tpfa, sol1d_box, "tpfa", "box");
+    // fem - tpfa
+    writeProjection<Scalar>(feGridGeometry1, tpfaGridGeometry2, sol2d_fem, sol1d_tpfa, "fem", "tpfa");
+    // fem - box
+    writeProjection<Scalar>(feGridGeometry1, boxGridGeometry2, sol2d_fem, sol1d_box, "fem", "box");
+    // tpfa - fem
+    writeProjection<Scalar>(tpfaGridGeometry1, feGridGeometry2, sol2d_tpfa, sol1d_fem, "tpfa", "fem");
+
+    return 0;
+}
+// //////////////////////////////////
+//   Error handler
+// /////////////////////////////////
+catch (Dune::Exception &e) {
+
+    std::cout << e << std::endl;
+    return 1;
+}
diff --git a/test/references/test_projection_2d1d_box_box_1d.csv b/test/references/test_projection_2d1d_box_box_1d.csv
new file mode 100644
index 0000000000000000000000000000000000000000..6f79a83904152582c7af5578159090cf47bd6ec4
--- /dev/null
+++ b/test/references/test_projection_2d1d_box_box_1d.csv
@@ -0,0 +1,14 @@
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diff --git a/test/references/test_projection_2d1d_box_box_2d.csv b/test/references/test_projection_2d1d_box_box_2d.csv
new file mode 100644
index 0000000000000000000000000000000000000000..6197ca93b3d710bba2772da7de4daa191386c202
--- /dev/null
+++ b/test/references/test_projection_2d1d_box_box_2d.csv
@@ -0,0 +1,121 @@
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diff --git a/test/references/test_projection_2d1d_box_tpfa_1d.csv b/test/references/test_projection_2d1d_box_tpfa_1d.csv
new file mode 100644
index 0000000000000000000000000000000000000000..5035330ff9436ed316ac9bef525d190b7d8f45b0
--- /dev/null
+++ b/test/references/test_projection_2d1d_box_tpfa_1d.csv
@@ -0,0 +1,13 @@
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diff --git a/test/references/test_projection_2d1d_box_tpfa_2d.csv b/test/references/test_projection_2d1d_box_tpfa_2d.csv
new file mode 100644
index 0000000000000000000000000000000000000000..c68fe4ee3ec3d32ddb0a96978c898429be32ce48
--- /dev/null
+++ b/test/references/test_projection_2d1d_box_tpfa_2d.csv
@@ -0,0 +1,121 @@
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diff --git a/test/references/test_projection_2d1d_fem_box_1d.csv b/test/references/test_projection_2d1d_fem_box_1d.csv
new file mode 100644
index 0000000000000000000000000000000000000000..6f79a83904152582c7af5578159090cf47bd6ec4
--- /dev/null
+++ b/test/references/test_projection_2d1d_fem_box_1d.csv
@@ -0,0 +1,14 @@
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diff --git a/test/references/test_projection_2d1d_fem_box_2d.csv b/test/references/test_projection_2d1d_fem_box_2d.csv
new file mode 100644
index 0000000000000000000000000000000000000000..6197ca93b3d710bba2772da7de4daa191386c202
--- /dev/null
+++ b/test/references/test_projection_2d1d_fem_box_2d.csv
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