diff --git a/ProcessLib/HeatConduction/Tests.cmake b/ProcessLib/HeatConduction/Tests.cmake
index e41ebb662c7..5277158dec8 100644
--- a/ProcessLib/HeatConduction/Tests.cmake
+++ b/ProcessLib/HeatConduction/Tests.cmake
@@ -379,7 +379,7 @@ AddTest(
     TESTER vtkdiff
     DIFF_DATA
     square_1e2_axi_ts_10_t_1.000000.vtu square_1e2_axi_ts_10_t_1.000000.vtu temperature temperature 2e-15 0
-    square_1e2_axi_ts_10_t_1.000000.vtu square_1e2_axi_ts_10_t_1.000000.vtu heat_flux heat_flux 1e-14 0
+    square_1e2_axi_ts_10_t_1.000000.vtu square_1e2_axi_ts_10_t_1.000000.vtu heat_flux heat_flux 2e-14 0
     REQUIREMENTS NOT OGS_USE_MPI
 )
 # WEDGE 1x1 HEAT CONDUCTION TEST -- same setup as above test but in cartesian coordinates
diff --git a/ProcessLib/RichardsMechanics/Tests.cmake b/ProcessLib/RichardsMechanics/Tests.cmake
index dc9ba762df6..1a4e6ea8af6 100644
--- a/ProcessLib/RichardsMechanics/Tests.cmake
+++ b/ProcessLib/RichardsMechanics/Tests.cmake
@@ -60,9 +60,9 @@ AddTest(
     confined_compression_fully_saturated_ts_120_t_1000.000000.vtu confined_compression_fully_saturated_restart_ts_100_t_1000.000000.vtu epsilon epsilon 5e-14 0
     confined_compression_fully_saturated_ts_420_t_4000.000000.vtu confined_compression_fully_saturated_restart_ts_400_t_4000.000000.vtu epsilon epsilon 5e-14 0
 
-    confined_compression_fully_saturated_ts_20_t_100.000000.vtu confined_compression_fully_saturated_restart_ts_0_t_100.000000.vtu saturation saturation 2.5e-15 0
-    confined_compression_fully_saturated_ts_120_t_1000.000000.vtu confined_compression_fully_saturated_restart_ts_100_t_1000.000000.vtu saturation saturation 2.5e-15 0
-    confined_compression_fully_saturated_ts_420_t_4000.000000.vtu confined_compression_fully_saturated_restart_ts_400_t_4000.000000.vtu saturation saturation 2.5e-15 0
+    confined_compression_fully_saturated_ts_20_t_100.000000.vtu confined_compression_fully_saturated_restart_ts_0_t_100.000000.vtu saturation saturation 3e-15 0
+    confined_compression_fully_saturated_ts_120_t_1000.000000.vtu confined_compression_fully_saturated_restart_ts_100_t_1000.000000.vtu saturation saturation 3e-15 0
+    confined_compression_fully_saturated_ts_420_t_4000.000000.vtu confined_compression_fully_saturated_restart_ts_400_t_4000.000000.vtu saturation saturation 3e-15 0
 
     confined_compression_fully_saturated_ts_20_t_100.000000.vtu confined_compression_fully_saturated_restart_ts_0_t_100.000000.vtu velocity velocity 1e-16 0
     confined_compression_fully_saturated_ts_120_t_1000.000000.vtu confined_compression_fully_saturated_restart_ts_100_t_1000.000000.vtu velocity velocity 1e-16 0
diff --git a/Tests/Data/LIE/Mechanics/mohr_coulomb_load_path_nu0p3.prj b/Tests/Data/LIE/Mechanics/mohr_coulomb_load_path_nu0p3.prj
index d3f637d55c3..41e84ecb3f3 100644
--- a/Tests/Data/LIE/Mechanics/mohr_coulomb_load_path_nu0p3.prj
+++ b/Tests/Data/LIE/Mechanics/mohr_coulomb_load_path_nu0p3.prj
@@ -308,7 +308,7 @@
         <vtkdiff>
             <regex>out_mohr_coulomb_load_path_nu0p3_ts_(.*)_t_2.500000.vtu</regex>
             <field>sigma</field>
-            <absolute_tolerance>7.0e-3</absolute_tolerance>
+            <absolute_tolerance>8.0e-3</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
diff --git a/Tests/Data/Mechanics/Ehlers/MFront/two_material_ids_single_solid.prj b/Tests/Data/Mechanics/Ehlers/MFront/two_material_ids_single_solid.prj
index 66bd7ecbdf0..14b838883dd 100644
--- a/Tests/Data/Mechanics/Ehlers/MFront/two_material_ids_single_solid.prj
+++ b/Tests/Data/Mechanics/Ehlers/MFront/two_material_ids_single_solid.prj
@@ -208,13 +208,13 @@
         <vtkdiff>
             <regex>two_material_ids_single_solid_t_.*.vtu</regex>
             <field>sigma</field>
-            <absolute_tolerance>2e-13</absolute_tolerance>
+            <absolute_tolerance>3e-13</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>two_material_ids_single_solid_t_.*.vtu</regex>
             <field>epsilon</field>
-            <absolute_tolerance>2e-15</absolute_tolerance>
+            <absolute_tolerance>3e-15</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
@@ -232,7 +232,7 @@
         <vtkdiff>
             <regex>two_material_ids_single_solid_t_.*.vtu</regex>
             <field>NodalForces</field>
-            <absolute_tolerance>5e-13</absolute_tolerance>
+            <absolute_tolerance>6e-13</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
     </test_definition>
diff --git a/Tests/Data/Mechanics/ModifiedCamClay/square_1e0_shear.prj b/Tests/Data/Mechanics/ModifiedCamClay/square_1e0_shear.prj
index 234ce8cc65d..69f3aa85238 100644
--- a/Tests/Data/Mechanics/ModifiedCamClay/square_1e0_shear.prj
+++ b/Tests/Data/Mechanics/ModifiedCamClay/square_1e0_shear.prj
@@ -235,7 +235,7 @@
             <file>square_1e0_shear_ts_100_t_1.000000.vtu</file>
             <field>sigma</field>
             <absolute_tolerance>1e-12</absolute_tolerance>
-            <relative_tolerance>1e-13</relative_tolerance>
+            <relative_tolerance>2e-13</relative_tolerance>
         </vtkdiff>
         <!--material-specific internal variable-->
         <vtkdiff>
diff --git a/Tests/Data/RichardsMechanics/double_porosity_swelling.prj b/Tests/Data/RichardsMechanics/double_porosity_swelling.prj
index 2949eecc1fd..e35add3e617 100644
--- a/Tests/Data/RichardsMechanics/double_porosity_swelling.prj
+++ b/Tests/Data/RichardsMechanics/double_porosity_swelling.prj
@@ -352,7 +352,7 @@
         <vtkdiff>
             <regex>double_porosity_swelling_.*.vtu</regex>
             <field>porosity</field>
-            <absolute_tolerance>2e-5</absolute_tolerance>
+            <absolute_tolerance>2.1e-5</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
diff --git a/Tests/Data/RichardsMechanics/orthotropic_swelling_xy.prj b/Tests/Data/RichardsMechanics/orthotropic_swelling_xy.prj
index b25c3885d5b..8379c4333ba 100644
--- a/Tests/Data/RichardsMechanics/orthotropic_swelling_xy.prj
+++ b/Tests/Data/RichardsMechanics/orthotropic_swelling_xy.prj
@@ -324,8 +324,8 @@
         <vtkdiff>
             <regex>orthotropic_swelling_xy_ts_.*.vtu</regex>
             <field>saturation</field>
-            <absolute_tolerance>2e-15</absolute_tolerance>
-            <relative_tolerance>1e-15</relative_tolerance>
+            <absolute_tolerance>4e-15</absolute_tolerance>
+            <relative_tolerance>4e-15</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>orthotropic_swelling_xy_ts_.*.vtu</regex>
@@ -342,7 +342,7 @@
         <vtkdiff>
             <regex>orthotropic_swelling_xy_ts_.*.vtu</regex>
             <field>swelling_stress</field>
-            <absolute_tolerance>1e-15</absolute_tolerance>
+            <absolute_tolerance>2e-15</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
diff --git a/Tests/Data/TH2M/H2M/OrthotropicSwelling/square.prj b/Tests/Data/TH2M/H2M/OrthotropicSwelling/square.prj
index 0726ab51ab7..de0f4825519 100644
--- a/Tests/Data/TH2M/H2M/OrthotropicSwelling/square.prj
+++ b/Tests/Data/TH2M/H2M/OrthotropicSwelling/square.prj
@@ -464,8 +464,8 @@
         <vtkdiff>
             <regex>square_ts_.*.vtu</regex>
             <field>saturation</field>
-            <absolute_tolerance>2e-15</absolute_tolerance>
-            <relative_tolerance>1e-15</relative_tolerance>
+            <absolute_tolerance>3e-15</absolute_tolerance>
+            <relative_tolerance>4e-15</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>square_ts_.*.vtu</regex>
@@ -482,7 +482,7 @@
         <vtkdiff>
             <regex>square_ts_.*.vtu</regex>
             <field>swelling_stress</field>
-            <absolute_tolerance>1e-15</absolute_tolerance>
+            <absolute_tolerance>2e-15</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
diff --git a/Tests/Data/TH2M/HM/Confined_Compression/HM_confined_compression_gas.prj b/Tests/Data/TH2M/HM/Confined_Compression/HM_confined_compression_gas.prj
index 91676a26672..193620a6d76 100644
--- a/Tests/Data/TH2M/HM/Confined_Compression/HM_confined_compression_gas.prj
+++ b/Tests/Data/TH2M/HM/Confined_Compression/HM_confined_compression_gas.prj
@@ -515,8 +515,8 @@
         <vtkdiff>
             <regex>HM_confined_compression_gas_ts_.*.vtu</regex>
             <field>porosity</field>
-            <absolute_tolerance>1e-15</absolute_tolerance>
-            <relative_tolerance>1e-15</relative_tolerance>
+            <absolute_tolerance>2e-15</absolute_tolerance>
+            <relative_tolerance>2e-15</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>HM_confined_compression_gas_ts_.*.vtu</regex>
diff --git a/Tests/Data/TH2M/HM/Confined_Compression/HM_confined_compression_liquid.prj b/Tests/Data/TH2M/HM/Confined_Compression/HM_confined_compression_liquid.prj
index 97001751570..7791d571bf4 100644
--- a/Tests/Data/TH2M/HM/Confined_Compression/HM_confined_compression_liquid.prj
+++ b/Tests/Data/TH2M/HM/Confined_Compression/HM_confined_compression_liquid.prj
@@ -522,8 +522,8 @@
         <vtkdiff>
             <regex>HM_confined_compression_liquid_ts_.*.vtu</regex>
             <field>porosity</field>
-            <absolute_tolerance>1e-15</absolute_tolerance>
-            <relative_tolerance>1e-15</relative_tolerance>
+            <absolute_tolerance>2e-15</absolute_tolerance>
+            <relative_tolerance>2e-15</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>HM_confined_compression_liquid_ts_.*.vtu</regex>
diff --git a/Tests/Data/TH2M/HM/flow_fully_saturated.prj b/Tests/Data/TH2M/HM/flow_fully_saturated.prj
index 36903d0786e..4c1072d2563 100644
--- a/Tests/Data/TH2M/HM/flow_fully_saturated.prj
+++ b/Tests/Data/TH2M/HM/flow_fully_saturated.prj
@@ -468,14 +468,14 @@
         <vtkdiff>
             <regex>flow_fully_saturated_ts_.*.vtu</regex>
             <field>liquid_density</field>
-            <absolute_tolerance>3e-15</absolute_tolerance>
-            <relative_tolerance>3e-15</relative_tolerance>
+            <absolute_tolerance>4e-15</absolute_tolerance>
+            <relative_tolerance>4e-15</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>flow_fully_saturated_ts_.*.vtu</regex>
             <field>gas_density</field>
-            <absolute_tolerance>3e-15</absolute_tolerance>
-            <relative_tolerance>3e-15</relative_tolerance>
+            <absolute_tolerance>4e-15</absolute_tolerance>
+            <relative_tolerance>4e-15</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>flow_fully_saturated_ts_.*.vtu</regex>
diff --git a/Tests/Data/TH2M/HM/flow_fully_saturated_gas.prj b/Tests/Data/TH2M/HM/flow_fully_saturated_gas.prj
index bc0ff250642..d6207efe014 100644
--- a/Tests/Data/TH2M/HM/flow_fully_saturated_gas.prj
+++ b/Tests/Data/TH2M/HM/flow_fully_saturated_gas.prj
@@ -519,14 +519,14 @@
         <vtkdiff>
             <regex>flow_fully_saturated_gas_ts_.*.vtu</regex>
             <field>liquid_density</field>
-            <absolute_tolerance>3e-15</absolute_tolerance>
-            <relative_tolerance>3e-15</relative_tolerance>
+            <absolute_tolerance>4e-15</absolute_tolerance>
+            <relative_tolerance>4e-15</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>flow_fully_saturated_gas_ts_.*.vtu</regex>
             <field>gas_density</field>
-            <absolute_tolerance>3e-15</absolute_tolerance>
-            <relative_tolerance>3e-15</relative_tolerance>
+            <absolute_tolerance>4e-15</absolute_tolerance>
+            <relative_tolerance>4e-15</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>flow_fully_saturated_gas_ts_.*.vtu</regex>