diff --git a/test/porousmediumflow/1p/implicit/pointsources/timeindependent/CMakeLists.txt b/test/porousmediumflow/1p/implicit/pointsources/timeindependent/CMakeLists.txt
index 06d7f95dddbb8ce28fbc3afe6c9b185c604bc750..3908a97f03736c99074bf789eb9ed5d900eb7c26 100644
--- a/test/porousmediumflow/1p/implicit/pointsources/timeindependent/CMakeLists.txt
+++ b/test/porousmediumflow/1p/implicit/pointsources/timeindependent/CMakeLists.txt
@@ -1,4 +1,5 @@
 add_input_file_links("params.input")
+dune_symlink_to_source_files(FILES grids)
 
 dune_add_test(NAME test_1p_pointsources_timeindependent_tpfa
               LABELS porousmediumflow 1p
@@ -20,6 +21,33 @@ dune_add_test(NAME test_1p_pointsources_timeindependent_box
                                ${CMAKE_CURRENT_BINARY_DIR}/test_1p_pointsources_timeindependent_box-00001.vtu
                        --command "${CMAKE_CURRENT_BINARY_DIR}/test_1p_pointsources_timeindependent_box params.input -Problem.Name test_1p_pointsources_timeindependent_box")
 
+dune_add_test(NAME test_1p_pointsources_timeindependent_tpfa_prism
+              LABELS porousmediumflow 1p
+              SOURCES main.cc
+              CMAKE_GUARD dune-uggrid_FOUND
+              COMPILE_DEFINITIONS GRIDTYPE=Dune::UGGrid<3>
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              COMPILE_DEFINITIONS TYPETAG=OnePSingularityCCTpfa
+              CMD_ARGS --script fuzzy
+                       --files ${CMAKE_SOURCE_DIR}/test/references/test_1p_pointsources_timeindependent_tpfa_prism-reference.vtu
+                               ${CMAKE_CURRENT_BINARY_DIR}/test_1p_pointsources_timeindependent_tpfa_prism-00001.vtu
+                       --command "${CMAKE_CURRENT_BINARY_DIR}/test_1p_pointsources_timeindependent_tpfa_prism params.input
+                                                                            -Problem.Name test_1p_pointsources_timeindependent_tpfa_prism
+                                                                            -Grid.File ./grids/well_prism.msh")
+
+dune_add_test(NAME test_1p_pointsources_timeindependent_box_prism
+              LABELS porousmediumflow 1p
+              SOURCES main.cc
+              CMAKE_GUARD dune-uggrid_FOUND
+              COMPILE_DEFINITIONS GRIDTYPE=Dune::UGGrid<3>
+              COMMAND ${CMAKE_SOURCE_DIR}/bin/testing/runtest.py
+              COMPILE_DEFINITIONS TYPETAG=OnePSingularityBox
+              CMD_ARGS --script fuzzy
+                       --files ${CMAKE_SOURCE_DIR}/test/references/test_1p_pointsources_timeindependent_box_prism-reference.vtu
+                               ${CMAKE_CURRENT_BINARY_DIR}/test_1p_pointsources_timeindependent_box_prism-00001.vtu
+                       --command "${CMAKE_CURRENT_BINARY_DIR}/test_1p_pointsources_timeindependent_box_prism params.input
+                                                                            -Problem.Name test_1p_pointsources_timeindependent_box_prism
+                                                                            -Grid.File ./grids/well_prism.msh")
 
 #install sources
 install(FILES
diff --git a/test/porousmediumflow/1p/implicit/pointsources/timeindependent/grids/well_prism.msh b/test/porousmediumflow/1p/implicit/pointsources/timeindependent/grids/well_prism.msh
new file mode 100644
index 0000000000000000000000000000000000000000..c853a5308991f206364bf2f5392711baee7441c3
--- /dev/null
+++ b/test/porousmediumflow/1p/implicit/pointsources/timeindependent/grids/well_prism.msh
@@ -0,0 +1,9239 @@
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+$EndElements
diff --git a/test/porousmediumflow/1p/implicit/pointsources/timeindependent/problem.hh b/test/porousmediumflow/1p/implicit/pointsources/timeindependent/problem.hh
index 0359127b9d3ae46287ecc268b54339722aceaf3f..b432e989985edf4c1bf43a96850a84039e970b59 100644
--- a/test/porousmediumflow/1p/implicit/pointsources/timeindependent/problem.hh
+++ b/test/porousmediumflow/1p/implicit/pointsources/timeindependent/problem.hh
@@ -25,6 +25,9 @@
 #ifndef DUMUX_1P_SINGULARITY_PROBLEM_HH
 #define DUMUX_1P_SINGULARITY_PROBLEM_HH
 
+#if HAVE_UG
+#include <dune/grid/uggrid.hh>
+#endif
 #include <dune/grid/yaspgrid.hh>
 
 #include <dumux/discretization/cctpfa.hh>
@@ -36,6 +39,10 @@
 
 #include "../spatialparams.hh"
 
+#ifndef GRIDTYPE // default to yasp grid if not provided by CMake
+#define GRIDTYPE Dune::YaspGrid<2, Dune::EquidistantOffsetCoordinates<GetPropType<TypeTag, Properties::Scalar>, 2> >
+#endif
+
 namespace Dumux {
 template <class TypeTag>
 class OnePSingularityProblem;
@@ -58,8 +65,7 @@ struct FluidSystem<TypeTag, TTag::OnePSingularity>
 
 // Set the grid type
 template<class TypeTag>
-struct Grid<TypeTag, TTag::OnePSingularity>
-{ using type = Dune::YaspGrid<2, Dune::EquidistantOffsetCoordinates<GetPropType<TypeTag, Properties::Scalar>, 2> >; };
+struct Grid<TypeTag, TTag::OnePSingularity> { using type = GRIDTYPE; };
 
 // Set the problem property
 template<class TypeTag>
diff --git a/test/references/test_1p_pointsources_timeindependent_box_prism-reference.vtu b/test/references/test_1p_pointsources_timeindependent_box_prism-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..13b90561fa22266f6494f6f9ee39c45af388b4d0
--- /dev/null
+++ b/test/references/test_1p_pointsources_timeindependent_box_prism-reference.vtu
@@ -0,0 +1,4625 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+  <UnstructuredGrid>
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diff --git a/test/references/test_1p_pointsources_timeindependent_tpfa_prism-reference.vtu b/test/references/test_1p_pointsources_timeindependent_tpfa_prism-reference.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..67032275952220bf4b41292243eb6dd0d12c60db
--- /dev/null
+++ b/test/references/test_1p_pointsources_timeindependent_tpfa_prism-reference.vtu
@@ -0,0 +1,4785 @@
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