diff --git a/ProcessLib/GroundwaterFlow/Tests.cmake b/ProcessLib/GroundwaterFlow/Tests.cmake
index eb3ea94bbd977ccd74d1b75529818134b25f0c35..d11b943543a2daca877eebc8c0705a4a08e2fa94 100644
--- a/ProcessLib/GroundwaterFlow/Tests.cmake
+++ b/ProcessLib/GroundwaterFlow/Tests.cmake
@@ -403,6 +403,21 @@ AddTest(
cube_1e3_neumann_pcs_0_ts_1_t_1_000000_2.vtu cube_1e3_neumann_pcs_0_ts_1_t_1_000000_2.vtu D1_left_front_N1_right pressure 1e-2 1e-2
)
+AddTest(
+ NAME ParallelFEM_GroundWaterFlow2D_NeumannBC
+ PATH EllipticPETSc
+ EXECUTABLE_ARGS square_1e1_neumann.prj
+ WRAPPER mpirun
+ WRAPPER_ARGS -np 2
+ TESTER vtkdiff
+ REQUIREMENTS OGS_USE_MPI
+ DIFF_DATA
+ square_1e1_neumann_pcs_0_ts_1_t_1_000000_0.vtu square_1e1_neumann_pcs_0_ts_1_t_1_000000_0.vtu D1_left_bottom_N1_right pressure 1e-2 0
+ square_1e1_neumann_pcs_0_ts_1_t_1_000000_1.vtu square_1e1_neumann_pcs_0_ts_1_t_1_000000_1.vtu D1_left_bottom_N1_right pressure 1e-2 0
+ square_1e1_neumann_pcs_0_ts_1_t_1_000000_0.vtu square_1e1_neumann_pcs_0_ts_1_t_1_000000_0.vtu pressure pressure 1e-14 0
+ square_1e1_neumann_pcs_0_ts_1_t_1_000000_1.vtu square_1e1_neumann_pcs_0_ts_1_t_1_000000_1.vtu pressure pressure 1e-14 0
+)
+
# Single core
# CUBE 1x1x1 GROUNDWATER FLOW TESTS
foreach(mesh_size 1e0 1e1 1e2 1e3)
diff --git a/Tests/Data/EllipticPETSc/square_1e1_neumann.prj b/Tests/Data/EllipticPETSc/square_1e1_neumann.prj
new file mode 100644
index 0000000000000000000000000000000000000000..14959d27e63af9f2f8528fc71670eda64b88a843
--- /dev/null
+++ b/Tests/Data/EllipticPETSc/square_1e1_neumann.prj
@@ -0,0 +1,123 @@
+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+ <meshes>
+ <mesh>square_1x1_quad_1e1.vtu</mesh>
+ <mesh>square_1x1_bottom.vtu</mesh>
+ <mesh>square_1x1_left.vtu</mesh>
+ <mesh>square_1x1_right.vtu</mesh>
+ <mesh>square_1x1_top.vtu</mesh>
+ </meshes>
+ <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="v"/>
+ </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>
+ <output>
+ <variables>
+ <variable> pressure </variable>
+ <variable> v </variable>
+ </variables>
+ </output>
+ <time_stepping>
+ <type>SingleStep</type>
+ </time_stepping>
+ </process>
+ </processes>
+ <output>
+ <type>VTK</type>
+ <prefix>square_1e1_neumann</prefix>
+ </output>
+ </time_loop>
+ <parameters>
+ <parameter>
+ <name>K</name>
+ <type>Constant</type>
+ <value>1</value>
+ </parameter>
+ <parameter>
+ <name>p0</name>
+ <type>Constant</type>
+ <value>0</value>
+ </parameter>
+ <parameter>
+ <name>p_neumann</name>
+ <type>Constant</type>
+ <value>1</value>
+ </parameter>
+ <parameter>
+ <name>p_Dirichlet</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>
+ <mesh>square_1x1_left</mesh>
+ <type>Dirichlet</type>
+ <parameter>p_Dirichlet</parameter>
+ </boundary_condition>
+ <boundary_condition>
+ <mesh>square_1x1_bottom</mesh>
+ <type>Dirichlet</type>
+ <parameter>p_Dirichlet</parameter>
+ </boundary_condition>
+ <boundary_condition>
+ <mesh>square_1x1_right</mesh>
+ <type>Neumann</type>
+ <parameter>p_neumann</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>
+</OpenGeoSysProject>
diff --git a/Tests/Data/EllipticPETSc/square_1e1_neumann_pcs_0_ts_1_t_1_000000_0.vtu b/Tests/Data/EllipticPETSc/square_1e1_neumann_pcs_0_ts_1_t_1_000000_0.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..4cc4bc8275fd018b6d5309e6a2a31edbd94d5132
--- /dev/null
+++ b/Tests/Data/EllipticPETSc/square_1e1_neumann_pcs_0_ts_1_t_1_000000_0.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:ba74277b0b85ea38855f76a2ea68bbca2680d711e4ee8aed868eaedcfac76fdf
+size 2764
diff --git a/Tests/Data/EllipticPETSc/square_1e1_neumann_pcs_0_ts_1_t_1_000000_1.vtu b/Tests/Data/EllipticPETSc/square_1e1_neumann_pcs_0_ts_1_t_1_000000_1.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..178050c3f2cce6f089c7165f9a198893363e808d
--- /dev/null
+++ b/Tests/Data/EllipticPETSc/square_1e1_neumann_pcs_0_ts_1_t_1_000000_1.vtu
@@ -0,0 +1,3 @@
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diff --git a/Tests/Data/EllipticPETSc/square_1x1_bottom.vtu b/Tests/Data/EllipticPETSc/square_1x1_bottom.vtu
new file mode 100644
index 0000000000000000000000000000000000000000..dd30b2c8b9f2d68233347b39f55ea830ee03d480
--- /dev/null
+++ b/Tests/Data/EllipticPETSc/square_1x1_bottom.vtu
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
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diff --git a/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_cell_properties_cfg2.bin b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_cell_properties_cfg2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..865c3a5cd345dc29f5c71d7b5a0a94c97ecf5fe3
--- /dev/null
+++ b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_cell_properties_cfg2.bin
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
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diff --git a/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_cell_properties_val2.bin b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_cell_properties_val2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..758d4c3fc7f3162b65176b4d2e4a322dd00d7aff
--- /dev/null
+++ b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_cell_properties_val2.bin
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
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diff --git a/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_msh_cfg2.bin b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_msh_cfg2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..1214fe4b6f0f6c18e9657c17bb2054a26244318d
--- /dev/null
+++ b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_msh_cfg2.bin
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+version https://git-lfs.github.com/spec/v1
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diff --git a/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_msh_ele2.bin b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_msh_ele2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..35bb9a835ecc7265f006901ec80ced43e7b8519b
--- /dev/null
+++ b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_msh_ele2.bin
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+size 144
diff --git a/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_msh_ele_g2.bin b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_msh_ele_g2.bin
new file mode 100644
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diff --git a/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_msh_nod2.bin b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_msh_nod2.bin
new file mode 100644
index 0000000000000000000000000000000000000000..81780412404e700857fcf560877c9b36fecfb218
--- /dev/null
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diff --git a/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_node_properties_cfg2.bin b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_node_properties_cfg2.bin
new file mode 100644
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--- /dev/null
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diff --git a/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_node_properties_val2.bin b/Tests/Data/EllipticPETSc/square_1x1_bottom_partitioned_node_properties_val2.bin
new file mode 100644
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diff --git a/Tests/Data/EllipticPETSc/square_1x1_left.vtu b/Tests/Data/EllipticPETSc/square_1x1_left.vtu
new file mode 100644
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--- /dev/null
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diff --git a/Tests/Data/EllipticPETSc/square_1x1_left_partitioned_cell_properties_cfg2.bin b/Tests/Data/EllipticPETSc/square_1x1_left_partitioned_cell_properties_cfg2.bin
new file mode 100644
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--- /dev/null
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new file mode 100644
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--- /dev/null
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