diff --git a/dumux/io/vtkmultiwriter.hh b/dumux/io/vtkmultiwriter.hh
index af9f1d5bc61c378daa6930ce2266daaae3426e27..97ee6a8caca12c3ecd0bb61683407b9d4ac2d81e 100644
--- a/dumux/io/vtkmultiwriter.hh
+++ b/dumux/io/vtkmultiwriter.hh
@@ -122,11 +122,16 @@ public:
     template <class VectorField>
     void addVertexData(VectorField *field, const char *name)
     {
-#ifndef NDEBUG
         // make sure the field is well defined
-        for (int i = 0; i < field->size(); ++i)
+        for (int i = 0; i < field->size(); ++i) {
             Valgrind::CheckDefined((*field)[i]);
-#endif
+
+            // set values which are too small to 0 to avoid problems
+            // with paraview
+            if (std::abs((*field)[i]) < FLT_MIN)
+                (*field)[i] = 0.0;
+        }
+
         curWriter_->addVertexData(*field, name);
     }