diff --git a/ProcessLib/HydroMechanics/HydroMechanicsFEM-impl.h b/ProcessLib/HydroMechanics/HydroMechanicsFEM-impl.h
index 0030c9d3cc7aea383fd5a3c628a8a07a795aba18..457acd7770bf972740ceec22623ac509f552f9d4 100644
--- a/ProcessLib/HydroMechanics/HydroMechanicsFEM-impl.h
+++ b/ProcessLib/HydroMechanics/HydroMechanicsFEM-impl.h
@@ -158,6 +158,12 @@ void HydroMechanicsLocalAssembler<ShapeFunctionDisplacement,
             displacement_size, pressure_size>::Zero(displacement_size,
                                                     pressure_size);
 
+    typename ShapeMatricesTypeDisplacement::template MatrixType<
+        pressure_size, displacement_size>
+        Kpu = ShapeMatricesTypeDisplacement::template MatrixType<
+            pressure_size, displacement_size>::Zero(pressure_size,
+                                                    displacement_size);
+
     double const& dt = _process_data.dt;
 
     ParameterLib::SpatialPosition x_position;
@@ -230,17 +236,18 @@ void HydroMechanicsLocalAssembler<ShapeFunctionDisplacement,
         //
         // pressure equation, pressure part.
         //
-        laplace_p.noalias() += dNdx_p.transpose() * K_over_mu * dNdx_p * w;
+        laplace_p.noalias() +=
+            rho_fr * dNdx_p.transpose() * K_over_mu * dNdx_p * w;
 
-        storage_p.noalias() += N_p.transpose() * S * N_p * w;
+        storage_p.noalias() += rho_fr * N_p.transpose() * S * N_p * w;
 
         local_rhs.template segment<pressure_size>(pressure_index).noalias() +=
-            dNdx_p.transpose() * rho_fr * K_over_mu * b * w;
+            dNdx_p.transpose() * rho_fr * rho_fr * K_over_mu * b * w;
 
         //
         // pressure equation, displacement part.
         //
-        // Reusing Kup.transpose().
+        Kpu.noalias() += rho_fr * alpha * N_p.transpose() * identity2.transpose() * B * w;
     }
     // displacement equation, pressure part
     local_Jac
@@ -258,11 +265,11 @@ void HydroMechanicsLocalAssembler<ShapeFunctionDisplacement,
     local_Jac
         .template block<pressure_size, displacement_size>(pressure_index,
                                                           displacement_index)
-        .noalias() = Kup.transpose() / dt;
+        .noalias() = Kpu / dt;
 
     // pressure equation
     local_rhs.template segment<pressure_size>(pressure_index).noalias() -=
-        laplace_p * p + storage_p * p_dot + Kup.transpose() * u_dot;
+        laplace_p * p + storage_p * p_dot + Kpu * u_dot;
 
     // displacement equation
     local_rhs.template segment<displacement_size>(displacement_index)
diff --git a/ProcessLib/HydroMechanics/Tests.cmake b/ProcessLib/HydroMechanics/Tests.cmake
index 97ef56b68ab12810365bc501dfca681e5a4a24df..605593d8baf616953343d9fc7e8ef956c4fa392d 100644
--- a/ProcessLib/HydroMechanics/Tests.cmake
+++ b/ProcessLib/HydroMechanics/Tests.cmake
@@ -249,7 +249,7 @@ AddTest(
     TESTER vtkdiff
     REQUIREMENTS NOT OGS_USE_MPI
     DIFF_DATA
-    hm2_1Dcolumn1_pcs_0_ts_120_t_6.000000.vtu hm2_1Dcolumn1_pcs_0_ts_120_t_6.000000.vtu pressure pressure 1.0e-10 0.0
+    hm2_1Dcolumn1_pcs_0_ts_120_t_6.000000.vtu hm2_1Dcolumn1_pcs_0_ts_120_t_6.000000.vtu pressure pressure 5.0e-10 0.0
     hm2_1Dcolumn1_pcs_0_ts_120_t_6.000000.vtu hm2_1Dcolumn1_pcs_0_ts_120_t_6.000000.vtu displacement displacement 1.0e-10 0.0
     hm2_1Dcolumn1_pcs_0_ts_120_t_6.000000.vtu hm2_1Dcolumn1_pcs_0_ts_120_t_6.000000.vtu sigma_xx sigma_xx 1.0e-9 0.0
     hm2_1Dcolumn1_pcs_0_ts_120_t_6.000000.vtu hm2_1Dcolumn1_pcs_0_ts_120_t_6.000000.vtu sigma_yy sigma_yy 1.0e-9 0.0
@@ -351,7 +351,7 @@ AddTest(
     REQUIREMENTS NOT OGS_USE_MPI
     DIFF_DATA
     expected_square_1e2_UC_early_pcs_0_ts_10_t_1.000000.vtu square_1e2_UC_early_pcs_0_ts_10_t_1.000000.vtu displacement displacement 1e-11 1e-16
-    expected_square_1e2_UC_early_pcs_0_ts_10_t_1.000000.vtu square_1e2_UC_early_pcs_0_ts_10_t_1.000000.vtu pressure pressure 1e-11 1e-16
+    expected_square_1e2_UC_early_pcs_0_ts_10_t_1.000000.vtu square_1e2_UC_early_pcs_0_ts_10_t_1.000000.vtu pressure pressure 1e-10 1e-16
 )
 # HydroMechanics; Small deformation, linear poroelastic (unconfined compression late) the drainage process is finished and the displacement of the porous media is only a result of solid properties.
 AddTest(
diff --git a/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2.prj b/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2.prj
index 7fc9e2aa0a65a4628a0d66d441912fd71fb837af..0e74896a34523ded0a654aaeb7b27790478edfb3 100644
--- a/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2.prj
+++ b/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2.prj
@@ -253,7 +253,7 @@
     <linear_solvers>
         <linear_solver>
             <name>general_linear_solver</name>
-            <lis>-i bicg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <lis>-i bicg -p ilu -tol 1e-16 -maxiter 10000</lis>
             <eigen>
                 <solver_type>BiCGSTAB</solver_type>
                 <precon_type>ILUT</precon_type>
diff --git a/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_120_t_1000.000000.vtu b/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_120_t_1000.000000.vtu
index 537e94192547ea6a17fb09f407d62fc7f7fa00b4..02eab81ba9aa2e53d386246b5123363e6f7b8ba5 100644
--- a/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_120_t_1000.000000.vtu
+++ b/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_120_t_1000.000000.vtu
@@ -1,3 +1,3 @@
 version https://git-lfs.github.com/spec/v1
-oid sha256:0b3a1cc0ba1b4e1403c73abd1bbf4e59a5d02b8f910312c7ff1169497708763c
-size 36381
+oid sha256:4060867638d917b545966c69e615c6f81d69ce7e5beb0169484f9563e5072f43
+size 36856
diff --git a/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_1_t_5.000000.vtu b/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_1_t_5.000000.vtu
index 53198af58f6f6a229c259dbf9cd6f02d84516ade..df50282a9d332c582a312fc3f75475eda87b7d37 100644
--- a/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_1_t_5.000000.vtu
+++ b/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_1_t_5.000000.vtu
@@ -1,3 +1,3 @@
 version https://git-lfs.github.com/spec/v1
-oid sha256:e68238d8160c4b5bc280d49c3856fa139bc720c94538af6b5c74908ae57f7d4d
-size 35972
+oid sha256:63370ea6b3f8dfb7d852bd132f1710420e06ec0c0ecb61fece8555e5f1f77ded
+size 36752
diff --git a/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_20_t_100.000000.vtu b/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_20_t_100.000000.vtu
index 31c46b8f0f13009bfaa6e77c0de7bc947a596c6a..364a483b2d93c358dfd077a63c4e0519f3f82792 100644
--- a/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_20_t_100.000000.vtu
+++ b/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_20_t_100.000000.vtu
@@ -1,3 +1,3 @@
 version https://git-lfs.github.com/spec/v1
-oid sha256:6b2a55261b638241e2cedc923779fd8be9f09ce676e3713068139e21d5c0d696
-size 33155
+oid sha256:9721735b7f6dcd1429cd4759142f3a6e536743520a3d0563ab4fbb7d3b45ea7c
+size 33872
diff --git a/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_420_t_4000.000000.vtu b/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_420_t_4000.000000.vtu
index 6fceceb02bc9c300c1aca808af9b5736373e2cda..fc70e057618a11fe969b82115af925ea53ba1d43 100644
--- a/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_420_t_4000.000000.vtu
+++ b/Tests/Data/HydroMechanics/Linear/Confined_Compression/square_1e2_pcs_0_ts_420_t_4000.000000.vtu
@@ -1,3 +1,3 @@
 version https://git-lfs.github.com/spec/v1
-oid sha256:735cdbe865eeb4320bbd913fd0abb2c6f6c00b39cc5d786ddaffadadcde62423
-size 41019
+oid sha256:7a8d95ec8beb20aaec442614f088e7b6c22233f74a7eeccc282418b09079456a
+size 41528
diff --git a/Tests/Data/HydroMechanics/Linear/Gravity/flow_gravity.prj b/Tests/Data/HydroMechanics/Linear/Gravity/flow_gravity.prj
index fca464fc47a54f8990cbe11bb619830a32315588..ebb4682dc862ca31af7139b796278c3ef0d997a4 100644
--- a/Tests/Data/HydroMechanics/Linear/Gravity/flow_gravity.prj
+++ b/Tests/Data/HydroMechanics/Linear/Gravity/flow_gravity.prj
@@ -156,7 +156,7 @@
 		<parameter>
             <name>flux_in</name>
             <type>Constant</type>
-            <value>1e-5</value>
+            <value>1e-2</value>
         </parameter>
     </parameters>
     <process_variables>
diff --git a/Tests/Data/HydroMechanics/Verification/hm1_1Dbeam.prj b/Tests/Data/HydroMechanics/Verification/hm1_1Dbeam.prj
index 6635984dccc045741847a0db3d22d81bbb5eede8..f459664d1a92d5697627a094c099fdcb5293d3d2 100755
--- a/Tests/Data/HydroMechanics/Verification/hm1_1Dbeam.prj
+++ b/Tests/Data/HydroMechanics/Verification/hm1_1Dbeam.prj
@@ -40,7 +40,7 @@
                 <secondary_variable type="static" internal_name="epsilon_xz" output_name="epsilon_xz"/>
                 <secondary_variable type="static" internal_name="epsilon_yz" output_name="epsilon_yz"/>
             </secondary_variables>
-            <specific_body_force> 0 0 -9.81 </specific_body_force>
+            <specific_body_force> 0 0 0 </specific_body_force>
         </process>
     </processes>
     <time_loop>
@@ -182,7 +182,7 @@
             <group_id_property>MaterialIDs</group_id_property>
             <index_values>
                 <index>0</index>
-                <value>0</value>
+                <value>1</value>
             </index_values>
         </parameter>
         <parameter>
@@ -207,7 +207,7 @@
         <parameter>
             <name>rho_liquid</name>
             <type>Constant</type>
-            <value>0</value>
+            <value>1</value>
         </parameter>
         <parameter>
             <name>zero</name>
diff --git a/Tests/Data/HydroMechanics/Verification/hm1_2Dsquare.prj b/Tests/Data/HydroMechanics/Verification/hm1_2Dsquare.prj
index 7e8096f84e7e7e5cb79fdecee97c7518646d0868..f4c24762767bc3d08dd2d76b18ba41da7d503acc 100755
--- a/Tests/Data/HydroMechanics/Verification/hm1_2Dsquare.prj
+++ b/Tests/Data/HydroMechanics/Verification/hm1_2Dsquare.prj
@@ -40,7 +40,7 @@
                 <secondary_variable type="static" internal_name="epsilon_xz" output_name="epsilon_xz"/>
                 <secondary_variable type="static" internal_name="epsilon_yz" output_name="epsilon_yz"/>
             </secondary_variables>
-            <specific_body_force> 0 0 -9.81 </specific_body_force>
+            <specific_body_force> 0 0 0 </specific_body_force>
         </process>
     </processes>
     <time_loop>
@@ -181,7 +181,7 @@
             <group_id_property>MaterialIDs</group_id_property>
             <index_values>
                 <index>0</index>
-                <value>0</value>
+                <value>1</value>
             </index_values>
         </parameter>
         <parameter>
@@ -206,7 +206,7 @@
         <parameter>
             <name>rho_liquid</name>
             <type>Constant</type>
-            <value>0</value>
+            <value>1</value>
         </parameter>
         <parameter>
             <name>zero</name>
diff --git a/Tests/Data/HydroMechanics/Verification/hm1_3Dcube.prj b/Tests/Data/HydroMechanics/Verification/hm1_3Dcube.prj
index fb5efe559f6ca44a4dae76373a92cfa62ff7fbc3..8523394a9896cca04dec4cca2c8d4663fa1d8e9f 100755
--- a/Tests/Data/HydroMechanics/Verification/hm1_3Dcube.prj
+++ b/Tests/Data/HydroMechanics/Verification/hm1_3Dcube.prj
@@ -40,7 +40,7 @@
                 <secondary_variable type="static" internal_name="epsilon_xz" output_name="epsilon_xz"/>
                 <secondary_variable type="static" internal_name="epsilon_yz" output_name="epsilon_yz"/>
             </secondary_variables>
-            <specific_body_force> 0 0 -9.81 </specific_body_force>
+            <specific_body_force> 0 0 0 </specific_body_force>
         </process>
     </processes>
     <time_loop>
@@ -181,7 +181,7 @@
             <group_id_property>MaterialIDs</group_id_property>
             <index_values>
                 <index>0</index>
-                <value>0</value>
+                <value>1</value>
             </index_values>
         </parameter>
         <parameter>
@@ -206,7 +206,7 @@
         <parameter>
             <name>rho_liquid</name>
             <type>Constant</type>
-            <value>0</value>
+            <value>1</value>
         </parameter>
         <parameter>
             <name>zero</name>
diff --git a/Tests/Data/HydroMechanics/Verification/hm2_1D1bt.prj b/Tests/Data/HydroMechanics/Verification/hm2_1D1bt.prj
index df8fd1ab73e5183601b44ca6ff5bdf9730be5419..a79b55245f1bcd1ebfe0dafc16d1e0b4f9aac3fc 100755
--- a/Tests/Data/HydroMechanics/Verification/hm2_1D1bt.prj
+++ b/Tests/Data/HydroMechanics/Verification/hm2_1D1bt.prj
@@ -39,7 +39,7 @@
                <secondary_variable type="static" internal_name="epsilon_xz" output_name="epsilon_xz"/>
                <secondary_variable type="static" internal_name="epsilon_yz" output_name="epsilon_yz"/>
             </secondary_variables>
-            <specific_body_force>0 0 -9.81</specific_body_force>
+            <specific_body_force>0 0 0</specific_body_force>
         </process>
     </processes>
     <time_loop>
@@ -135,7 +135,7 @@
             <group_id_property>MaterialIDs</group_id_property>
             <index_values>
                 <index>0</index>
-                <value>0</value>
+                <value>1</value>
             </index_values>
         </parameter>
         <parameter>
@@ -160,7 +160,7 @@
         <parameter>
             <name>rho_liquid</name>
             <type>Constant</type>
-            <value> 0 </value>
+            <value> 1 </value>
         </parameter>
         <parameter>
             <name>zero</name>
diff --git a/Tests/Data/HydroMechanics/Verification/hm2_1D2bt.prj b/Tests/Data/HydroMechanics/Verification/hm2_1D2bt.prj
index 2f53cb873a82d4b809e68156da4c2d608cc8e56f..996b4ac1791f2521d471a2f499ee9b2e4e8181c5 100755
--- a/Tests/Data/HydroMechanics/Verification/hm2_1D2bt.prj
+++ b/Tests/Data/HydroMechanics/Verification/hm2_1D2bt.prj
@@ -39,7 +39,7 @@
                 <secondary_variable type="static" internal_name="epsilon_xz" output_name="epsilon_xz"/>
                 <secondary_variable type="static" internal_name="epsilon_yz" output_name="epsilon_yz"/>
             </secondary_variables>
-            <specific_body_force>0 0 -9.81</specific_body_force>
+            <specific_body_force>0 0 0</specific_body_force>
         </process>
     </processes>
     <time_loop>
@@ -135,7 +135,7 @@
             <group_id_property>MaterialIDs</group_id_property>
             <index_values>
                 <index>0</index>
-                <value>0</value>
+                <value>1</value>
             </index_values>
         </parameter>
         <parameter>
@@ -160,7 +160,7 @@
         <parameter>
             <name>rho_liquid</name>
             <type>Constant</type>
-            <value> 0 </value>
+            <value> 1 </value>
         </parameter>
         <parameter>
             <name>zero</name>
diff --git a/Tests/Data/HydroMechanics/Verification/hm2_1Dbiot.prj b/Tests/Data/HydroMechanics/Verification/hm2_1Dbiot.prj
index 6052c88e46f8defbf8a8bb158ec9bd9e0b38829d..70ae31c01cfdc56ed750e0f16a1add6427faddbf 100755
--- a/Tests/Data/HydroMechanics/Verification/hm2_1Dbiot.prj
+++ b/Tests/Data/HydroMechanics/Verification/hm2_1Dbiot.prj
@@ -39,7 +39,7 @@
                 <secondary_variable type="static" internal_name="epsilon_xz" output_name="epsilon_xz"/>
                 <secondary_variable type="static" internal_name="epsilon_yz" output_name="epsilon_yz"/>
             </secondary_variables>
-            <specific_body_force>0 0 -9.81</specific_body_force>
+            <specific_body_force>0 0 0</specific_body_force>
         </process>
     </processes>
     <time_loop>
@@ -135,7 +135,7 @@
             <group_id_property>MaterialIDs</group_id_property>
             <index_values>
                 <index>0</index>
-                <value>0</value>
+                <value>1</value>
             </index_values>
         </parameter>
         <parameter>
@@ -160,7 +160,7 @@
         <parameter>
             <name>rho_liquid</name>
             <type>Constant</type>
-            <value> 0 </value>
+            <value> 1 </value>
         </parameter>
         <parameter>
             <name>zero</name>
diff --git a/Tests/Data/HydroMechanics/Verification/hm2_1Dcolumn1.prj b/Tests/Data/HydroMechanics/Verification/hm2_1Dcolumn1.prj
index fc6b5873cfbc7c8701c9f2518bb5a147edbee5e0..1399cd7996f42d351c13b7dd377c1725bb3135fd 100755
--- a/Tests/Data/HydroMechanics/Verification/hm2_1Dcolumn1.prj
+++ b/Tests/Data/HydroMechanics/Verification/hm2_1Dcolumn1.prj
@@ -39,7 +39,7 @@
                 <secondary_variable type="static" internal_name="epsilon_xz" output_name="epsilon_xz"/>
                 <secondary_variable type="static" internal_name="epsilon_yz" output_name="epsilon_yz"/>
             </secondary_variables>
-            <specific_body_force>0 0 -9.81</specific_body_force>
+            <specific_body_force>0 0 0</specific_body_force>
         </process>
     </processes>
     <time_loop>
@@ -135,7 +135,7 @@
             <group_id_property>MaterialIDs</group_id_property>
             <index_values>
                 <index>0</index>
-                <value>0</value>
+                <value>1</value>
             </index_values>
         </parameter>
         <parameter>
@@ -160,7 +160,7 @@
         <parameter>
             <name>rho_liquid</name>
             <type>Constant</type>
-            <value> 0 </value>
+            <value> 1 </value>
         </parameter>
         <parameter>
             <name>zero</name>
diff --git a/Tests/Data/HydroMechanics/Verification/hm2_1Dcolumn2.prj b/Tests/Data/HydroMechanics/Verification/hm2_1Dcolumn2.prj
index 5a87230f66e66d2ae0efdda91c7efd590aed572c..8c1a5a4f5b8ba79b5c81329fe83382fdc01dd392 100755
--- a/Tests/Data/HydroMechanics/Verification/hm2_1Dcolumn2.prj
+++ b/Tests/Data/HydroMechanics/Verification/hm2_1Dcolumn2.prj
@@ -39,7 +39,7 @@
                 <secondary_variable type="static" internal_name="epsilon_xz" output_name="epsilon_xz"/>
                 <secondary_variable type="static" internal_name="epsilon_yz" output_name="epsilon_yz"/>
             </secondary_variables>
-            <specific_body_force>0 0 -9.81</specific_body_force>
+            <specific_body_force>0 0 0</specific_body_force>
         </process>
     </processes>
     <time_loop>
@@ -139,7 +139,7 @@
             <group_id_property>MaterialIDs</group_id_property>
             <index_values>
                 <index>0</index>
-                <value>0</value>
+                <value>1</value>
             </index_values>
         </parameter>
         <parameter>
@@ -164,7 +164,7 @@
         <parameter>
             <name>rho_liquid</name>
             <type>Constant</type>
-            <value> 0 </value>
+            <value> 1 </value>
         </parameter>
         <parameter>
             <name>zero</name>
diff --git a/Tests/Data/HydroMechanics/Verification/hm2_2Dmandel.prj b/Tests/Data/HydroMechanics/Verification/hm2_2Dmandel.prj
index d95141e171116b175e58a1c7625ddbadbbc34028..4861e69894065806fc7a593f4d91ea8b4459ca8b 100755
--- a/Tests/Data/HydroMechanics/Verification/hm2_2Dmandel.prj
+++ b/Tests/Data/HydroMechanics/Verification/hm2_2Dmandel.prj
@@ -39,7 +39,7 @@
                 <secondary_variable type="static" internal_name="epsilon_xz" output_name="epsilon_xz"/>
                 <secondary_variable type="static" internal_name="epsilon_yz" output_name="epsilon_yz"/>
             </secondary_variables>
-            <specific_body_force>0 0 -9.81</specific_body_force>
+            <specific_body_force>0 0 0</specific_body_force>
         </process>
     </processes>
     <time_loop>
@@ -139,7 +139,7 @@
             <group_id_property>MaterialIDs</group_id_property>
             <index_values>
                 <index>0</index>
-                <value>0</value>
+                <value>1</value>
             </index_values>
         </parameter>
         <parameter>
@@ -164,7 +164,7 @@
         <parameter>
             <name>rho_liquid</name>
             <type>Constant</type>
-            <value> 0 </value>
+            <value> 1 </value>
         </parameter>
         <parameter>
             <name>zero</name>