diff --git a/dune/gdt/test/interpolations/boundary.hh b/dune/gdt/test/interpolations/boundary.hh
new file mode 100644
index 0000000000000000000000000000000000000000..b16e758de4181ab0255f3f245b7ed916db4128fb
--- /dev/null
+++ b/dune/gdt/test/interpolations/boundary.hh
@@ -0,0 +1,102 @@
+// This file is part of the dune-gdt project:
+// https://github.com/dune-community/dune-gdt
+// Copyright 2010-2018 dune-gdt developers and contributors. All rights reserved.
+// License: Dual licensed as BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
+// or GPL-2.0+ (http://opensource.org/licenses/gpl-license)
+// with "runtime exception" (http://www.dune-project.org/license.html)
+// Authors:
+// Felix Schindler (2019)
+
+#ifndef DUNE_GDT_TEST_INTERPOLATIONS_BOUNDARY_HH
+#define DUNE_GDT_TEST_INTERPOLATIONS_BOUNDARY_HH
+
+#include <dune/xt/common/fvector.hh>
+#include <dune/xt/common/string.hh>
+#include <dune/xt/common/test/gtest/gtest.h>
+#include <dune/xt/grid/boundaryinfo/normalbased.hh>
+#include <dune/xt/grid/gridprovider/cube.hh>
+#include <dune/xt/grid/structuredgridfactory.hh>
+#include <dune/xt/grid/type_traits.hh>
+#include <dune/xt/functions/constant.hh>
+#include <dune/xt/functions/generic/function.hh>
+
+#include <dune/gdt/discretefunction/default.hh>
+#include <dune/gdt/interpolations/boundary.hh>
+#include <dune/gdt/local/bilinear-forms/integrals.hh>
+#include <dune/gdt/local/integrands/product.hh>
+#include <dune/gdt/norms.hh>
+#include <dune/gdt/spaces/h1/continuous-lagrange.hh>
+
+namespace Dune {
+namespace GDT {
+namespace Test {
+
+
+template <class G>
+struct BoundaryInterpolationOnLeafViewTest : public ::testing::Test
+{
+ static_assert(XT::Grid::is_grid<G>::value, "");
+
+ using GV = typename G::LeafGridView;
+ using D = typename GV::ctype;
+ static const constexpr size_t d = GV::dimension;
+ using E = XT::Grid::extract_entity_t<GV>;
+ using I = XT::Grid::extract_intersection_t<GV>;
+ using M = XT::LA::IstlRowMajorSparseMatrix<double>;
+ using V = XT::LA::IstlDenseVector<double>;
+
+ std::shared_ptr<XT::Grid::GridProvider<G>> grid_provider;
+ std::shared_ptr<XT::Functions::ConstantFunction<d>> source;
+ std::shared_ptr<XT::Grid::NormalBasedBoundaryInfo<I>> boundary_info;
+ std::shared_ptr<ContinuousLagrangeSpace<GV>> space;
+ std::shared_ptr<DiscreteFunction<V, GV>> range;
+ std::shared_ptr<XT::Functions::GenericFunction<d>> expected_range;
+
+ virtual std::shared_ptr<XT::Grid::GridProvider<G>> make_grid()
+ {
+ return std::make_shared<XT::Grid::GridProvider<G>>(
+ XT::Grid::make_cube_grid<G>(XT::Common::from_string<FieldVector<double, d>>("[-1 0 0 0]"),
+ XT::Common::from_string<FieldVector<double, d>>("[1 1 1 1]"),
+ XT::Common::from_string<std::array<unsigned int, d>>("[2 1 1 1]")));
+ }
+
+ void SetUp() override
+ {
+ grid_provider = make_grid();
+ space =
+ std::make_shared<ContinuousLagrangeSpace<GV>>(make_continuous_lagrange_space(grid_provider->leaf_view(), 1));
+ source = std::make_shared<XT::Functions::ConstantFunction<d>>(1.);
+ range = std::make_shared<DiscreteFunction<V, GV>>(*space);
+ expected_range = std::make_shared<XT::Functions::GenericFunction<d>>([](const auto&) { return 1; },
+ [](const auto& x, const auto&) {
+ if (x[0] > 0)
+ return x[0];
+ else
+ return 0.;
+ });
+ boundary_info = std::make_shared<XT::Grid::NormalBasedBoundaryInfo<I>>();
+ boundary_info->register_new_normal(XT::Common::from_string<FieldVector<double, d>>("[1 0 0 0]"),
+ new XT::Grid::DirichletBoundary());
+ } // ... SetUp(...)
+
+ void interpolates_correctly()
+ {
+ interpolate(source->template as_grid_function<E>(),
+ *range,
+ space->grid_view(),
+ *boundary_info,
+ XT::Grid::DirichletBoundary());
+ const auto expected_L2_error = 1e-15;
+ const auto l2_error = compute_l2_norm(space->grid_view(), expected_range->template as_grid_function<E>() - *range);
+ EXPECT_LT(l2_error, expected_L2_error)
+ << "XT::Common::Test::get_unique_test_name() = '" << XT::Common::Test::get_unique_test_name() << "'";
+
+ } // ... interpolates_correctly(...)
+}; // struct BoundaryInterpolationOnLeafViewTest
+
+
+} // namespace Test
+} // namespace GDT
+} // namespace Dune
+
+#endif // DUNE_GDT_TEST_INTERPOLATIONS_BOUNDARY_HH
diff --git a/dune/gdt/test/interpolations/interpolations_boundary__cubic_2d_grids.cc b/dune/gdt/test/interpolations/interpolations_boundary__cubic_2d_grids.cc
new file mode 100644
index 0000000000000000000000000000000000000000..592f326c2841b47188de525c62425ac6cf4c4003
--- /dev/null
+++ b/dune/gdt/test/interpolations/interpolations_boundary__cubic_2d_grids.cc
@@ -0,0 +1,35 @@
+// This file is part of the dune-gdt project:
+// https://github.com/dune-community/dune-gdt
+// Copyright 2010-2018 dune-gdt developers and contributors. All rights reserved.
+// License: Dual licensed as BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
+// or GPL-2.0+ (http://opensource.org/licenses/gpl-license)
+// with "runtime exception" (http://www.dune-project.org/license.html)
+// Authors:
+// Felix Schindler (2019)
+
+#include <dune/xt/common/test/main.hxx> // <- this one has to come first (includes the config.h)!
+
+#include <dune/xt/grid/grids.hh>
+
+#include "boundary.hh"
+
+
+using Cubic2dGrids = ::testing::Types<YASP_2D_EQUIDISTANT_OFFSET
+#if HAVE_DUNE_ALUGRID
+ ,
+ ALU_2D_CUBE
+#endif
+#if HAVE_DUNE_UGGRID
+ ,
+ UG_2D
+#endif
+ >;
+
+
+template <class G>
+using BoundaryInterpolation = Dune::GDT::Test::BoundaryInterpolationOnLeafViewTest<G>;
+TYPED_TEST_CASE(BoundaryInterpolation, Cubic2dGrids);
+TYPED_TEST(BoundaryInterpolation, interpolates_correctly)
+{
+ this->interpolates_correctly();
+}
diff --git a/dune/gdt/test/interpolations/interpolations_boundary__cubic_3d_grids.cc b/dune/gdt/test/interpolations/interpolations_boundary__cubic_3d_grids.cc
new file mode 100644
index 0000000000000000000000000000000000000000..8e443daa4327709a5e7d62776e0f5f29ba73ac45
--- /dev/null
+++ b/dune/gdt/test/interpolations/interpolations_boundary__cubic_3d_grids.cc
@@ -0,0 +1,35 @@
+// This file is part of the dune-gdt project:
+// https://github.com/dune-community/dune-gdt
+// Copyright 2010-2018 dune-gdt developers and contributors. All rights reserved.
+// License: Dual licensed as BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
+// or GPL-2.0+ (http://opensource.org/licenses/gpl-license)
+// with "runtime exception" (http://www.dune-project.org/license.html)
+// Authors:
+// Felix Schindler (2019)
+
+#include <dune/xt/common/test/main.hxx> // <- this one has to come first (includes the config.h)!
+
+#include <dune/xt/grid/grids.hh>
+
+#include "boundary.hh"
+
+
+using Cubic3dGrids = ::testing::Types<YASP_3D_EQUIDISTANT_OFFSET
+#if HAVE_DUNE_ALUGRID
+ ,
+ ALU_3D_CUBE
+#endif
+#if HAVE_DUNE_UGGRID
+ ,
+ UG_3D
+#endif
+ >;
+
+
+template <class G>
+using BoundaryInterpolation = Dune::GDT::Test::BoundaryInterpolationOnLeafViewTest<G>;
+TYPED_TEST_CASE(BoundaryInterpolation, Cubic3dGrids);
+TYPED_TEST(BoundaryInterpolation, interpolates_correctly)
+{
+ this->interpolates_correctly();
+}
diff --git a/dune/gdt/test/interpolations/interpolations_boundary__cubic_4d_grids.cc b/dune/gdt/test/interpolations/interpolations_boundary__cubic_4d_grids.cc
new file mode 100644
index 0000000000000000000000000000000000000000..137b72ac1f46add550682368fd67a0b9df78d8bc
--- /dev/null
+++ b/dune/gdt/test/interpolations/interpolations_boundary__cubic_4d_grids.cc
@@ -0,0 +1,26 @@
+// This file is part of the dune-gdt project:
+// https://github.com/dune-community/dune-gdt
+// Copyright 2010-2018 dune-gdt developers and contributors. All rights reserved.
+// License: Dual licensed as BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
+// or GPL-2.0+ (http://opensource.org/licenses/gpl-license)
+// with "runtime exception" (http://www.dune-project.org/license.html)
+// Authors:
+// Felix Schindler (2019)
+
+#include <dune/xt/common/test/main.hxx> // <- this one has to come first (includes the config.h)!
+
+#include <dune/xt/grid/grids.hh>
+
+#include "boundary.hh"
+
+
+using Cubic4dGrids = ::testing::Types<YASP_4D_EQUIDISTANT_OFFSET>;
+
+
+template <class G>
+using BoundaryInterpolation = Dune::GDT::Test::BoundaryInterpolationOnLeafViewTest<G>;
+TYPED_TEST_CASE(BoundaryInterpolation, Cubic4dGrids);
+TYPED_TEST(BoundaryInterpolation, interpolates_correctly)
+{
+ this->interpolates_correctly();
+}
diff --git a/dune/gdt/test/interpolations/interpolations_boundary__simplicial_1d_grids.cc b/dune/gdt/test/interpolations/interpolations_boundary__simplicial_1d_grids.cc
new file mode 100644
index 0000000000000000000000000000000000000000..61bc231b0b4d714350f79a95258aa682918ba873
--- /dev/null
+++ b/dune/gdt/test/interpolations/interpolations_boundary__simplicial_1d_grids.cc
@@ -0,0 +1,26 @@
+// This file is part of the dune-gdt project:
+// https://github.com/dune-community/dune-gdt
+// Copyright 2010-2018 dune-gdt developers and contributors. All rights reserved.
+// License: Dual licensed as BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
+// or GPL-2.0+ (http://opensource.org/licenses/gpl-license)
+// with "runtime exception" (http://www.dune-project.org/license.html)
+// Authors:
+// Felix Schindler (2019)
+
+#include <dune/xt/common/test/main.hxx> // <- this one has to come first (includes the config.h)!
+
+#include <dune/xt/grid/grids.hh>
+
+#include "boundary.hh"
+
+
+using Simplicial1dGrids = ::testing::Types<ONED_1D, YASP_1D_EQUIDISTANT_OFFSET>;
+
+
+template <class G>
+using BoundaryInterpolation = Dune::GDT::Test::BoundaryInterpolationOnLeafViewTest<G>;
+TYPED_TEST_CASE(BoundaryInterpolation, Simplicial1dGrids);
+TYPED_TEST(BoundaryInterpolation, interpolates_correctly)
+{
+ this->interpolates_correctly();
+}
diff --git a/dune/gdt/test/interpolations/interpolations_boundary__simplicial_2d_grids.cc b/dune/gdt/test/interpolations/interpolations_boundary__simplicial_2d_grids.cc
new file mode 100644
index 0000000000000000000000000000000000000000..cd7bbc0c9f9239e02a8156958718dcb7c0ac51f9
--- /dev/null
+++ b/dune/gdt/test/interpolations/interpolations_boundary__simplicial_2d_grids.cc
@@ -0,0 +1,37 @@
+// This file is part of the dune-gdt project:
+// https://github.com/dune-community/dune-gdt
+// Copyright 2010-2018 dune-gdt developers and contributors. All rights reserved.
+// License: Dual licensed as BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
+// or GPL-2.0+ (http://opensource.org/licenses/gpl-license)
+// with "runtime exception" (http://www.dune-project.org/license.html)
+// Authors:
+// Felix Schindler (2019)
+
+#include <dune/xt/common/test/main.hxx> // <- this one has to come first (includes the config.h)!
+
+#include <dune/xt/grid/grids.hh>
+
+#include "boundary.hh"
+
+
+using Simplicial2dGrids = ::testing::Types<
+#if HAVE_DUNE_ALUGRID
+ ALU_2D_SIMPLEX_CONFORMING,
+ ALU_2D_SIMPLEX_NONCONFORMING
+#endif
+#if HAVE_DUNE_ALUGRID && HAVE_DUNE_UGGRID
+ ,
+#endif
+#if HAVE_DUNE_UGGRID
+ UG_2D
+#endif
+ >;
+
+
+template <class G>
+using BoundaryInterpolation = Dune::GDT::Test::BoundaryInterpolationOnLeafViewTest<G>;
+TYPED_TEST_CASE(BoundaryInterpolation, Simplicial2dGrids);
+TYPED_TEST(BoundaryInterpolation, interpolates_correctly)
+{
+ this->interpolates_correctly();
+}
diff --git a/dune/gdt/test/interpolations/interpolations_boundary__simplicial_3d_grids.cc b/dune/gdt/test/interpolations/interpolations_boundary__simplicial_3d_grids.cc
new file mode 100644
index 0000000000000000000000000000000000000000..2522bafeb107f298b7674063ab1fe27ec5779a5d
--- /dev/null
+++ b/dune/gdt/test/interpolations/interpolations_boundary__simplicial_3d_grids.cc
@@ -0,0 +1,37 @@
+// This file is part of the dune-gdt project:
+// https://github.com/dune-community/dune-gdt
+// Copyright 2010-2018 dune-gdt developers and contributors. All rights reserved.
+// License: Dual licensed as BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
+// or GPL-2.0+ (http://opensource.org/licenses/gpl-license)
+// with "runtime exception" (http://www.dune-project.org/license.html)
+// Authors:
+// Felix Schindler (2019)
+
+#include <dune/xt/common/test/main.hxx> // <- this one has to come first (includes the config.h)!
+
+#include <dune/xt/grid/grids.hh>
+
+#include "boundary.hh"
+
+
+using Simplicial3dGrids = ::testing::Types<
+#if HAVE_DUNE_ALUGRID
+ ALU_3D_SIMPLEX_CONFORMING,
+ ALU_3D_SIMPLEX_NONCONFORMING
+#endif
+#if HAVE_DUNE_ALUGRID && HAVE_DUNE_UGGRID
+ ,
+#endif
+#if HAVE_DUNE_UGGRID
+ UG_3D
+#endif
+ >;
+
+
+template <class G>
+using BoundaryInterpolation = Dune::GDT::Test::BoundaryInterpolationOnLeafViewTest<G>;
+TYPED_TEST_CASE(BoundaryInterpolation, Simplicial3dGrids);
+TYPED_TEST(BoundaryInterpolation, interpolates_correctly)
+{
+ this->interpolates_correctly();
+}