diff --git a/opm/grid/CpGrid.hpp b/opm/grid/CpGrid.hpp
index 7cbb066279..ab6f06ac82 100644
--- a/opm/grid/CpGrid.hpp
+++ b/opm/grid/CpGrid.hpp
@@ -1242,7 +1242,7 @@ namespace Dune
         /// \brief Get the Position of a vertex.
         /// \param vertex The index identifying the vertex.
         /// \return The coordinates of the vertex.
-        const Vector& vertexPosition(int vertex) const;
+        Vector vertexPosition(int vertex) const;
 
         /// \brief Get the area of a face.
         /// \param face The index identifying the face.
@@ -1250,12 +1250,12 @@ namespace Dune
 
         /// \brief Get the coordinates of the center of a face.
         /// \param face The index identifying the face.
-        const Vector& faceCentroid(int face) const;
+        Vector faceCentroid(int face) const;
 
         /// \brief Get the unit normal of a face.
         /// \param face The index identifying the face.
         /// \see faceCell
-        const Vector& faceNormal(int face) const;
+        Vector faceNormal(int face) const;
 
         /// \brief Get the volume of the cell.
         /// \param cell The index identifying the cell.
@@ -1263,7 +1263,7 @@ namespace Dune
 
         /// \brief Get the coordinates of the center of a cell.
         /// \param cell The index identifying the face.
-        const Vector& cellCentroid(int cell) const;
+        Vector cellCentroid(int cell) const;
 
         /// \brief An iterator over the centroids of the geometry of the entities.
         /// \tparam codim The co-dimension of the entities.
diff --git a/opm/grid/cpgrid/CpGrid.cpp b/opm/grid/cpgrid/CpGrid.cpp
index a77084222f..40d7267f38 100644
--- a/opm/grid/cpgrid/CpGrid.cpp
+++ b/opm/grid/cpgrid/CpGrid.cpp
@@ -1563,7 +1563,7 @@ const Dune::FieldVector<double,3> CpGrid::faceAreaNormalEcl(int face) const
     }
 }
 
-const Dune::FieldVector<double,3>& CpGrid::vertexPosition(int vertex) const
+Dune::FieldVector<double,3> CpGrid::vertexPosition(int vertex) const
 {
     return current_data_->back()->geomVector<3>()[cpgrid::EntityRep<3>(vertex, true)].center();
 }
@@ -1573,12 +1573,12 @@ double CpGrid::faceArea(int face) const
     return current_data_->back()->geomVector<1>()[cpgrid::EntityRep<1>(face, true)].volume();
 }
 
-const Dune::FieldVector<double,3>& CpGrid::faceCentroid(int face) const
+Dune::FieldVector<double,3> CpGrid::faceCentroid(int face) const
 {
     return current_data_->back()->geomVector<1>()[cpgrid::EntityRep<1>(face, true)].center();
 }
 
-const Dune::FieldVector<double,3>& CpGrid::faceNormal(int face) const
+Dune::FieldVector<double,3> CpGrid::faceNormal(int face) const
 {
     return current_data_->back()->face_normals_.get(face);
 }
@@ -1588,7 +1588,7 @@ double CpGrid::cellVolume(int cell) const
     return current_data_->back()->geomVector<0>()[cpgrid::EntityRep<0>(cell, true)].volume();
 }
 
-const Dune::FieldVector<double,3>& CpGrid::cellCentroid(int cell) const
+Dune::FieldVector<double,3> CpGrid::cellCentroid(int cell) const
 {
     return current_data_->back()->geomVector<0>()[cpgrid::EntityRep<0>(cell, true)].center();
 }
diff --git a/opm/grid/cpgrid/Entity.hpp b/opm/grid/cpgrid/Entity.hpp
index f60e23bc0f..8e9ce9171b 100644
--- a/opm/grid/cpgrid/Entity.hpp
+++ b/opm/grid/cpgrid/Entity.hpp
@@ -193,7 +193,7 @@ class Entity : public EntityRep<codim>
     }
 
     /// @brief Return the geometry of the entity (does not depend on its orientation).
-    const Geometry& geometry() const;
+    Geometry geometry() const;
 
     /// @brief Return the level of the entity in the grid hierarchy. Level = 0 represents the coarsest grid.
     int level() const;
@@ -422,7 +422,7 @@ unsigned int Entity<codim>::subEntities ( const unsigned int cc ) const
 }
 
 template <int codim>
-const typename Entity<codim>::Geometry& Entity<codim>::geometry() const
+typename Entity<codim>::Geometry Entity<codim>::geometry() const
 {
     return pgrid_->geomVector<codim>()[*this];
 }
diff --git a/opm/grid/cpgrid/Geometry.hpp b/opm/grid/cpgrid/Geometry.hpp
index a57505189f..bd959a36d6 100644
--- a/opm/grid/cpgrid/Geometry.hpp
+++ b/opm/grid/cpgrid/Geometry.hpp
@@ -128,7 +128,7 @@ namespace Dune
             }
 
             /// Returns the position of the vertex.
-            const GlobalCoordinate& global(const LocalCoordinate&) const
+            GlobalCoordinate global(const LocalCoordinate&) const
             {
                 return pos_;
             }
@@ -173,7 +173,7 @@ namespace Dune
             }
 
             /// Returns the centroid of the geometry.
-            const GlobalCoordinate& center() const
+            GlobalCoordinate center() const
             {
                 return pos_;
             }
@@ -273,7 +273,7 @@ namespace Dune
             }
 
             /// This method is meaningless for singular geometries.
-            const GlobalCoordinate& global(const LocalCoordinate&) const
+            GlobalCoordinate global(const LocalCoordinate&) const
             {
                 OPM_THROW(std::runtime_error, "Geometry::global() meaningless on singular geometry.");
             }
@@ -320,20 +320,20 @@ namespace Dune
             }
 
             /// Returns the centroid of the geometry.
-            const GlobalCoordinate& center() const
+            GlobalCoordinate center() const
             {
                 return pos_;
             }
 
             /// This method is meaningless for singular geometries.
-            const FieldMatrix<ctype, mydimension, coorddimension>&
+            FieldMatrix<ctype, mydimension, coorddimension>
             jacobianTransposed(const LocalCoordinate& /* local */) const
             {
                 OPM_THROW(std::runtime_error, "Meaningless to call jacobianTransposed() on singular geometries.");
             }
 
             /// This method is meaningless for singular geometries.
-            const FieldMatrix<ctype, coorddimension, mydimension>&
+            FieldMatrix<ctype, coorddimension, mydimension>
             jacobianInverseTransposed(const LocalCoordinate& /*local*/) const
             {
                 OPM_THROW(std::runtime_error, "Meaningless to call jacobianInverseTransposed() on singular geometries.");
@@ -527,7 +527,7 @@ namespace Dune
             }
 
             /// Returns the centroid of the geometry.
-            const GlobalCoordinate& center() const
+            GlobalCoordinate center() const
             {
                 return pos_;
             }
@@ -538,7 +538,7 @@ namespace Dune
             /// and {u_i} are the reference coordinates.
             /// g = g(u) = (g_1(u), g_2(u), g_3(u)), u=(u_1,u_2,u_3)
             /// g = map from (local) reference domain to global cell
-            const JacobianTransposed
+            JacobianTransposed
             jacobianTransposed(const LocalCoordinate& local_coord) const
             {
                 static_assert(mydimension == 3, "");
@@ -574,7 +574,7 @@ namespace Dune
             }
 
             /// @brief Inverse of Jacobian transposed. \see jacobianTransposed().
-            const JacobianInverseTransposed
+            JacobianInverseTransposed
             jacobianInverseTransposed(const LocalCoordinate& local_coord) const
             {
                 JacobianInverseTransposed Jti = jacobianTransposed(local_coord);
diff --git a/opm/grid/cpgrid/GridHelpers.cpp b/opm/grid/cpgrid/GridHelpers.cpp
index fe3a404b00..2ba9125ff2 100644
--- a/opm/grid/cpgrid/GridHelpers.cpp
+++ b/opm/grid/cpgrid/GridHelpers.cpp
@@ -147,9 +147,9 @@ beginFaceCentroids(const Dune::CpGrid& grid)
     return FaceCentroidTraits<Dune::CpGrid>::IteratorType(grid, 0);
 }
 
-const double* cellCentroid(const Dune::CpGrid& grid, int cell_index)
+Vector cellCentroid(const Dune::CpGrid& grid, int cell_index)
 {
-    return &(grid.cellCentroid(cell_index)[0]);
+    return grid.cellCentroid(cell_index);
 }
 
 double cellVolume(const  Dune::CpGrid& grid, int cell_index)
@@ -167,8 +167,7 @@ CellVolumeIterator endCellVolumes(const Dune::CpGrid& grid)
     return CellVolumeIterator(grid, numCells(grid));
 }
 
-const FaceCentroidTraits<Dune::CpGrid>::ValueType&
-faceCentroid(const Dune::CpGrid& grid, int face_index)
+Vector faceCentroid(const Dune::CpGrid& grid, int face_index)
 {
     return grid.faceCentroid(face_index);
 }
@@ -190,14 +189,14 @@ face2Vertices(const Dune::CpGrid& grid)
     return Dune::cpgrid::FaceVerticesContainerProxy(&grid);
 }
 
-const double* vertexCoordinates(const Dune::CpGrid& grid, int index)
+Vector vertexCoordinates(const Dune::CpGrid& grid, int index)
 {
-    return &(grid.vertexPosition(index)[0]);
+    return grid.vertexPosition(index);
 }
 
-const double* faceNormal(const Dune::CpGrid& grid, int face_index)
+Vector faceNormal(const Dune::CpGrid& grid, int face_index)
 {
-    return &(grid.faceNormal(face_index)[0]);
+    return grid.faceNormal(face_index);
 }
 
 double faceArea(const Dune::CpGrid& grid, int face_index)
diff --git a/opm/grid/cpgrid/GridHelpers.hpp b/opm/grid/cpgrid/GridHelpers.hpp
index c30dab6ef0..18e2562f04 100644
--- a/opm/grid/cpgrid/GridHelpers.hpp
+++ b/opm/grid/cpgrid/GridHelpers.hpp
@@ -328,10 +328,10 @@ struct Cell2FacesTraits<Dune::CpGrid>
     typedef Dune::cpgrid::Cell2FacesContainer Type;
 };
 /// \brief An iterator over the cell volumes.
-template<const Dune::FieldVector<double, 3>& (Dune::CpGrid::*Method)(int)const>
+template<Dune::FieldVector<double, 3> (Dune::CpGrid::*Method)(int)const>
 class CpGridCentroidIterator
     : public Dune::RandomAccessIteratorFacade<CpGridCentroidIterator<Method>, Dune::FieldVector<double, 3>,
-                                              const Dune::FieldVector<double, 3>&, int>
+                                              Dune::FieldVector<double, 3>, int>
 {
 public:
     /// \brief Creates an iterator.
@@ -341,7 +341,7 @@ class CpGridCentroidIterator
         : grid_(&grid), cell_index_(cell_index)
     {}
 
-    const Dune::FieldVector<double, 3>& dereference() const
+    Dune::FieldVector<double, 3> dereference() const
     {
         return std::mem_fn(Method)(*grid_, cell_index_);
     }
@@ -349,7 +349,7 @@ class CpGridCentroidIterator
     {
         ++cell_index_;
     }
-    const Dune::FieldVector<double, 3>& elementAt(int n) const
+    Dune::FieldVector<double, 3> elementAt(int n) const
     {
         return  std::mem_fn(Method)(*grid_, n);
     }
@@ -430,7 +430,7 @@ double cellCentroidCoordinate(const Dune::CpGrid& grid, int cell_index,
 /// \brief Get the centroid of a cell.
 /// \param grid The grid whose cell centroid we query.
 /// \param cell_index The index of the corresponding cell.
-const double* cellCentroid(const Dune::CpGrid& grid, int cell_index);
+Vector cellCentroid(const Dune::CpGrid& grid, int cell_index);
 
 /// \brief Get vertical position of cell center ("zcorn" average).
 /// \brief grid The grid.
@@ -531,8 +531,7 @@ beginFaceCentroids(const Dune::CpGrid& grid);
 /// \param grid The grid.
 /// \param face_index The index of the specific face.
 /// \param coordinate The coordinate index.
-const FaceCentroidTraits<Dune::CpGrid>::ValueType&
-faceCentroid(const Dune::CpGrid& grid, int face_index);
+Vector faceCentroid(const Dune::CpGrid& grid, int face_index);
 
 template<>
 struct FaceCellTraits<Dune::CpGrid>
@@ -559,9 +558,9 @@ face2Vertices(const Dune::CpGrid& grid);
 /// \brief Get the coordinates of a vertex of the grid.
 /// \param grid The grid the vertex is part of.
 /// \param index The index identifying the vertex.
-const double* vertexCoordinates(const Dune::CpGrid& grid, int index);
+Vector vertexCoordinates(const Dune::CpGrid& grid, int index);
 
-const double* faceNormal(const Dune::CpGrid& grid, int face_index);
+Vector faceNormal(const Dune::CpGrid& grid, int face_index);
 
 double faceArea(const Dune::CpGrid& grid, int face_index);
 
diff --git a/opm/grid/cpgrid/Intersection.hpp b/opm/grid/cpgrid/Intersection.hpp
index 2d6a376bb9..6354aa8696 100644
--- a/opm/grid/cpgrid/Intersection.hpp
+++ b/opm/grid/cpgrid/Intersection.hpp
@@ -158,7 +158,7 @@ namespace Dune
             /// @brief
             /// @todo Doc me!
             /// @return
-            const LocalGeometry& geometryInInside() const
+            LocalGeometry geometryInInside() const
             {
                 OPM_THROW(std::runtime_error, "This intersection class does not support geometryInInside().");
             }
@@ -168,7 +168,7 @@ namespace Dune
             /// @brief
             /// @todo Doc me!
             /// @return
-            const LocalGeometry& geometryInOutside() const
+            LocalGeometry geometryInOutside() const
             {
                 if (boundary()) {
                     OPM_THROW(std::runtime_error, "Cannot access geometryInOutside(), intersection is at a boundary.");
diff --git a/opm/grid/transmissibility/TransTpfa_impl.hpp b/opm/grid/transmissibility/TransTpfa_impl.hpp
index 8a943ec9e2..30a09934fb 100644
--- a/opm/grid/transmissibility/TransTpfa_impl.hpp
+++ b/opm/grid/transmissibility/TransTpfa_impl.hpp
@@ -87,7 +87,7 @@ tpfa_htrans_compute(const Grid* G, const double *perm, double *htrans)
             s = 2.0*(face_cells(*f, 0) == c) - 1.0;
             n = faceNormal(*G, *f);
             const double* nn=multiplyFaceNormalWithArea(*G, *f, n);
-            const double* fc = &(faceCentroid(*G, *f)[0]);
+            const auto fc = faceCentroid(*G, *f);
             dgemv_("No Transpose", &nrows, &ncols,
                    &a1, K, &ldA, nn, &incx, &a2, &Kn[0], &incy);
             maybeFreeFaceNormal(*G, nn);