diff --git a/Tests/Data/Mechanics/Linear/PythonPiston/piston.prj b/Tests/Data/Mechanics/Linear/PythonPiston/piston.prj
index ba576cce09c..6c168cea929 100644
--- a/Tests/Data/Mechanics/Linear/PythonPiston/piston.prj
+++ b/Tests/Data/Mechanics/Linear/PythonPiston/piston.prj
@@ -160,13 +160,13 @@
         <vtkdiff>
             <file>piston_ts_5_t_5.000000.vtu</file>
             <field>epsilon</field>
-            <absolute_tolerance>7e-15</absolute_tolerance>
+            <absolute_tolerance>1e-14</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
             <file>piston_ts_5_t_5.000000.vtu</file>
             <field>sigma</field>
-            <absolute_tolerance>1e-8</absolute_tolerance>
+            <absolute_tolerance>2e-8</absolute_tolerance>
             <relative_tolerance>0</relative_tolerance>
         </vtkdiff>
         <vtkdiff>
diff --git a/Tests/Data/Mechanics/ModifiedCamClay/triaxtest.prj b/Tests/Data/Mechanics/ModifiedCamClay/triaxtest.prj
index 0f06ed03824..102ea273fb5 100644
--- a/Tests/Data/Mechanics/ModifiedCamClay/triaxtest.prj
+++ b/Tests/Data/Mechanics/ModifiedCamClay/triaxtest.prj
@@ -285,6 +285,9 @@
                 <solver_type>SparseLU</solver_type>
                 <scaling>true</scaling>
             </eigen>
+            <petsc>
+                <parameters>-ksp_type richardson -pc_type lu</parameters>
+            </petsc>
         </linear_solver>
     </linear_solvers>
     <test_definition>
diff --git a/Tests/Data/Mechanics/ModifiedCamClay/triaxtest_original.prj b/Tests/Data/Mechanics/ModifiedCamClay/triaxtest_original.prj
index a6e8c715cc2..b0ae2c14133 100644
--- a/Tests/Data/Mechanics/ModifiedCamClay/triaxtest_original.prj
+++ b/Tests/Data/Mechanics/ModifiedCamClay/triaxtest_original.prj
@@ -280,6 +280,9 @@
                 <solver_type>SparseLU</solver_type>
                 <scaling>true</scaling>
             </eigen>
+            <petsc>
+                <parameters>-ksp_type richardson -pc_type lu</parameters>
+            </petsc>
         </linear_solver>
     </linear_solvers>
     <test_definition>