diff --git a/ProcessLib/TH2M/Tests.cmake b/ProcessLib/TH2M/Tests.cmake
index f2da84e1423ac4bc0fa606ab95beb13c59203d43..54da70cabf876aa48409c764179c28a2b9e705c3 100644
--- a/ProcessLib/TH2M/Tests.cmake
+++ b/ProcessLib/TH2M/Tests.cmake
@@ -358,7 +358,7 @@ AddTest(
     result_point_heatsource_ts_5_t_100000_000000_2.vtu result_point_heatsource_ts_5_t_100000_000000_2.vtu liquid_pressure_interpolated liquid_pressure_interpolated 7e-7 1e-3
     result_point_heatsource_ts_5_t_100000_000000_2.vtu result_point_heatsource_ts_5_t_100000_000000_2.vtu velocity_gas velocity_gas 1e-8 1e-8
     result_point_heatsource_ts_5_t_100000_000000_2.vtu result_point_heatsource_ts_5_t_100000_000000_2.vtu velocity_liquid velocity_liquid 1e-8 1e-8
-    result_point_heatsource_ts_5_t_100000_000000_2.vtu result_point_heatsource_ts_5_t_100000_000000_2.vtu sigma sigma 2e-4 4e-3
+    result_point_heatsource_ts_5_t_100000_000000_2.vtu result_point_heatsource_ts_5_t_100000_000000_2.vtu sigma sigma 2e-4 7e-3
     result_point_heatsource_ts_5_t_100000_000000_2.vtu result_point_heatsource_ts_5_t_100000_000000_2.vtu epsilon epsilon 1e-8 1e-8
     result_point_heatsource_ts_5_t_100000_000000_2.vtu result_point_heatsource_ts_5_t_100000_000000_2.vtu liquid_density liquid_density 1e-8 1e-8
     result_point_heatsource_ts_5_t_100000_000000_2.vtu result_point_heatsource_ts_5_t_100000_000000_2.vtu gas_density gas_density 1e-8 1e-8
diff --git a/Tests/Data/Mechanics/CreepWithHeterogeneousReferenceTemperature/arehs-salt-M_gravity_only_element_refT.prj b/Tests/Data/Mechanics/CreepWithHeterogeneousReferenceTemperature/arehs-salt-M_gravity_only_element_refT.prj
index 84fe10632061ab74c33ff0eead076cf923d85608..be2bac4a888253e4223816f416afd191633c08e5 100644
--- a/Tests/Data/Mechanics/CreepWithHeterogeneousReferenceTemperature/arehs-salt-M_gravity_only_element_refT.prj
+++ b/Tests/Data/Mechanics/CreepWithHeterogeneousReferenceTemperature/arehs-salt-M_gravity_only_element_refT.prj
@@ -31,8 +31,8 @@
                 <q>Q</q>
                 <nonlinear_solver>
                     <maximum_iterations>4000</maximum_iterations>
-                    <residuum_tolerance>3.0e-6</residuum_tolerance>
-                    <increment_tolerance>4.0e-7</increment_tolerance>
+                    <residuum_tolerance>5.0e-6</residuum_tolerance>
+                    <increment_tolerance>5.0e-7</increment_tolerance>
                 </nonlinear_solver>
             </constitutive_relation>
             <constitutive_relation id="3">
diff --git a/Tests/Data/TH2M/TH2/heatpipe/heat_pipe_rough.prj b/Tests/Data/TH2M/TH2/heatpipe/heat_pipe_rough.prj
index 45792566c244eeab3ef9ace69de25b8896a9e855..1a62479ae1fe0a8cb6bba3f60f3281b5586d2d2d 100644
--- a/Tests/Data/TH2M/TH2/heatpipe/heat_pipe_rough.prj
+++ b/Tests/Data/TH2M/TH2/heatpipe/heat_pipe_rough.prj
@@ -589,13 +589,13 @@
             <regex>results_heatpipe_rough_ts_.*.vtu</regex>
             <field>gas_pressure</field>
             <absolute_tolerance>1e-6</absolute_tolerance>
-            <relative_tolerance>0</relative_tolerance>
+            <relative_tolerance>1.e-6</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>results_heatpipe_rough_ts_.*.vtu</regex>
             <field>capillary_pressure</field>
             <absolute_tolerance>1e-6</absolute_tolerance>
-            <relative_tolerance>0</relative_tolerance>
+            <relative_tolerance>1.e-6</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>results_heatpipe_rough_ts_.*.vtu</regex>
diff --git a/Tests/Data/TH2M/TH2/heatpipe/heat_pipe_strict.prj b/Tests/Data/TH2M/TH2/heatpipe/heat_pipe_strict.prj
index c6d5041f3d55f709036c8534bfbc73bbda5bda3c..cd5fc6f9a9c6a45796db03a46f77e4846ea8b7e5 100644
--- a/Tests/Data/TH2M/TH2/heatpipe/heat_pipe_strict.prj
+++ b/Tests/Data/TH2M/TH2/heatpipe/heat_pipe_strict.prj
@@ -585,13 +585,13 @@
             <regex>results_heatpipe_strict_ts_.*.vtu</regex>
             <field>gas_pressure</field>
             <absolute_tolerance>1e-8</absolute_tolerance>
-            <relative_tolerance>0</relative_tolerance>
+            <relative_tolerance>1e-10</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>results_heatpipe_strict_ts_.*.vtu</regex>
             <field>capillary_pressure</field>
             <absolute_tolerance>1e-8</absolute_tolerance>
-            <relative_tolerance>0</relative_tolerance>
+            <relative_tolerance>1e-10</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <regex>results_heatpipe_strict_ts_.*.vtu</regex>