diff --git a/ProcessLib/GroundwaterFlow/Tests.cmake b/ProcessLib/GroundwaterFlow/Tests.cmake
index 4060516e9319545165b77a61dacd5f48d359ccb3..04989e1770cde3daef69be18bc2a8930a3d7e6ca 100644
--- a/ProcessLib/GroundwaterFlow/Tests.cmake
+++ b/ProcessLib/GroundwaterFlow/Tests.cmake
@@ -757,3 +757,7 @@ AddTest(
DIFF_DATA
square_1x1_quad_1e5.vtu square_1e5_volumetricsourceterm_pcs_0_ts_1_t_1.000000.vtu analytical_solution pressure 0.75e-4 1e-16
)
+
+if (NOT OGS_USE_MPI)
+ OgsTest(PROJECTFILE "Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_anisotropic.prj")
+endif() # OGS_USE_MPI
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_anisotropic.prj b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_anisotropic.prj
new file mode 100644
index 0000000000000000000000000000000000000000..873cfeda2410d23cfe29cb6433eef6317f615162
--- /dev/null
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_anisotropic.prj
@@ -0,0 +1,160 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+ <mesh>cube_1x1x1_hex_1e4_material_groups.vtu</mesh>
+ <geometry>cube_1x1x1.gml</geometry>
+ <processes>
+ <process>
+ <name>GW23</name>
+ <type>GROUNDWATER_FLOW</type>
+ <integration_order>2</integration_order>
+ <hydraulic_conductivity>K</hydraulic_conductivity>
+ <process_variables>
+ <process_variable>pressure</process_variable>
+ </process_variables>
+ <secondary_variables>
+ <secondary_variable type="static" internal_name="darcy_velocity" output_name="darcy_velocity"/>
+ </secondary_variables>
+ </process>
+ </processes>
+ <time_loop>
+ <processes>
+ <process ref="GW23">
+ <nonlinear_solver>basic_picard</nonlinear_solver>
+ <convergence_criterion>
+ <type>DeltaX</type>
+ <norm_type>NORM2</norm_type>
+ <abstol>1.e-6</abstol>
+ </convergence_criterion>
+ <time_discretization>
+ <type>BackwardEuler</type>
+ </time_discretization>
+ <time_stepping>
+ <type>SingleStep</type>
+ </time_stepping>
+ </process>
+ </processes>
+ <output>
+ <type>VTK</type>
+ <prefix>cube_1e4_anisotropic</prefix>
+ <variables>
+ <variable>pressure</variable>
+ <variable>darcy_velocity</variable>
+ </variables>
+ </output>
+ </time_loop>
+ <local_coordinate_system>
+ <basis_vector_0>e0</basis_vector_0>
+ <basis_vector_1>e1</basis_vector_1>
+ <basis_vector_2>e2</basis_vector_2>
+ </local_coordinate_system>
+ <parameters>
+ <parameter>
+ <name>e0</name>
+ <type>Constant</type>
+ <values>0.86602540378443864676 0 0.5</values>
+ </parameter>
+ <parameter>
+ <name>e1</name>
+ <type>Constant</type>
+ <values>0 1 0</values>
+ </parameter>
+ <parameter>
+ <name>e2</name>
+ <type>Constant</type>
+ <values>-0.5 0 0.86602540378443864676</values>
+ </parameter>
+ <parameter>
+ <name>K</name>
+ <type>Group</type>
+ <group_id_property>MaterialIDs</group_id_property>
+ <index_values>
+ <index>0</index>
+ <values>1 1 1</values>
+ </index_values>
+ <index_values>
+ <index>1</index>
+ <values>1 1 0.1</values>
+ </index_values>
+ <index_values>
+ <index>2</index>
+ <values>0.1 0.1 1</values>
+ </index_values>
+ <use_local_coordinate_system>true</use_local_coordinate_system>
+ </parameter>
+ <parameter>
+ <name>p0</name>
+ <type>Constant</type>
+ <value>0</value>
+ </parameter>
+ <parameter>
+ <name>p_Dirichlet_left</name>
+ <type>Constant</type>
+ <value>1</value>
+ </parameter>
+ <parameter>
+ <name>p_Dirichlet_right</name>
+ <type>Constant</type>
+ <value>-1</value>
+ </parameter>
+ </parameters>
+ <process_variables>
+ <process_variable>
+ <name>pressure</name>
+ <components>1</components>
+ <order>1</order>
+ <initial_condition>p0</initial_condition>
+ <boundary_conditions>
+ <boundary_condition>
+ <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+ <geometry>left</geometry>
+ <type>Dirichlet</type>
+ <parameter>p_Dirichlet_left</parameter>
+ </boundary_condition>
+ <boundary_condition>
+ <geometrical_set>cube_1x1x1_geometry</geometrical_set>
+ <geometry>right</geometry>
+ <type>Dirichlet</type>
+ <parameter>p_Dirichlet_right</parameter>
+ </boundary_condition>
+ </boundary_conditions>
+ </process_variable>
+ </process_variables>
+ <nonlinear_solvers>
+ <nonlinear_solver>
+ <name>basic_picard</name>
+ <type>Picard</type>
+ <max_iter>10</max_iter>
+ <linear_solver>general_linear_solver</linear_solver>
+ </nonlinear_solver>
+ </nonlinear_solvers>
+ <linear_solvers>
+ <linear_solver>
+ <name>general_linear_solver</name>
+ <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+ <eigen>
+ <solver_type>CG</solver_type>
+ <precon_type>DIAGONAL</precon_type>
+ <max_iteration_step>10000</max_iteration_step>
+ <error_tolerance>1e-16</error_tolerance>
+ </eigen>
+ <petsc>
+ <prefix>gw</prefix>
+ <parameters>-gw_ksp_type cg -gw_pc_type bjacobi -gw_ksp_rtol 1e-16 -gw_ksp_max_it 10000</parameters>
+ </petsc>
+ </linear_solver>
+ </linear_solvers>
+ <test_definition>
+ <vtkdiff>
+ <file>cube_1e4_anisotropic_pcs_0_ts_1_t_1.000000.vtu</file>
+ <field>pressure</field>
+ <absolute_tolerance>1e-14</absolute_tolerance>
+ <relative_tolerance>0</relative_tolerance>
+ </vtkdiff>
+ <vtkdiff>
+ <file>cube_1e4_anisotropic_pcs_0_ts_1_t_1.000000.vtu</file>
+ <field>darcy_velocity</field>
+ <absolute_tolerance>1e-13</absolute_tolerance>
+ <relative_tolerance>0</relative_tolerance>
+ </vtkdiff>
+ </test_definition>
+</OpenGeoSysProject>
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_anisotropic_pcs_0_ts_1_t_1.000000.vtu b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_anisotropic_pcs_0_ts_1_t_1.000000.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..9f30855f5a5bdb4604745096d11774ed5e52b815
--- /dev/null
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1e4_anisotropic_pcs_0_ts_1_t_1.000000.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ca0087cac718442365e68d5790e0d6c1dbea4b98f8181bcf680d4450d76e8d64
+size 601553
diff --git a/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1x1x1_hex_1e4_material_groups.vtu b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1x1x1_hex_1e4_material_groups.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..043da40d0ef8eea19aa6047b2b08bca71d2624d1
--- /dev/null
+++ b/Tests/Data/Elliptic/cube_1x1x1_GroundWaterFlow/cube_1x1x1_hex_1e4_material_groups.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:38ecf86d582cd8b5b154915c67b789f0cd2883d7f35f793f64c4541fd425fbf0
+size 1711591