diff --git a/opm/simulators/linalg/FlowLinearSolverParameters.hpp b/opm/simulators/linalg/FlowLinearSolverParameters.hpp
index f2019bccf..425c41a2c 100644
--- a/opm/simulators/linalg/FlowLinearSolverParameters.hpp
+++ b/opm/simulators/linalg/FlowLinearSolverParameters.hpp
@@ -45,6 +45,12 @@ template<class TypeTag, class MyTypeTag>
 struct LinearSolverReduction {
     using type = UndefinedProperty;
 };
+
+template<class TypeTag, class MyTypeTag>
+struct RelaxedLinearSolverReduction {
+    using type = UndefinedProperty;
+};
+    
 template<class TypeTag, class MyTypeTag>
 struct IluRelaxation {
     using type = UndefinedProperty;
@@ -126,6 +132,11 @@ struct LinearSolverReduction<TypeTag, TTag::FlowIstlSolverParams> {
     static constexpr type value = 1e-2;
 };
 template<class TypeTag>
+struct RelaxedLinearSolverReduction<TypeTag, TTag::FlowIstlSolverParams> {
+    using type = GetPropType<TypeTag, Scalar>;
+    static constexpr type value = 1e-2;
+};    
+template<class TypeTag>
 struct IluRelaxation<TypeTag, TTag::FlowIstlSolverParams> {
     using type = GetPropType<TypeTag, Scalar>;
     static constexpr type value = 0.9;
@@ -217,6 +228,7 @@ namespace Opm
     struct FlowLinearSolverParameters
     {
         double linear_solver_reduction_;
+        double relaxed_linear_solver_reduction_;
         double ilu_relaxation_;
         int    linear_solver_maxiter_;
         int    linear_solver_restart_;
@@ -242,6 +254,7 @@ namespace Opm
         {
             // TODO: these parameters have undocumented non-trivial dependencies
             linear_solver_reduction_ = EWOMS_GET_PARAM(TypeTag, double, LinearSolverReduction);
+            relaxed_linear_solver_reduction_ = EWOMS_GET_PARAM(TypeTag, double, RelaxedLinearSolverReduction);
             ilu_relaxation_ = EWOMS_GET_PARAM(TypeTag, double, IluRelaxation);
             linear_solver_maxiter_ = EWOMS_GET_PARAM(TypeTag, int, LinearSolverMaxIter);
             linear_solver_restart_ = EWOMS_GET_PARAM(TypeTag, int, LinearSolverRestart);
@@ -271,7 +284,8 @@ namespace Opm
         template <class TypeTag>
         static void registerParameters()
         {
-            EWOMS_REGISTER_PARAM(TypeTag, double, LinearSolverReduction, "The minimum reduction of the residual which the linear solver must achieve");
+            EWOMS_REGISTER_PARAM(TypeTag, double, LinearSolverReduction, "The minimum reduction of the residual which the linear solver must achieve should try to achive");
+            EWOMS_REGISTER_PARAM(TypeTag, double, RelaxedLinearSolverReduction, "The minimum reduction of the residual which the linear solver need to achieve for the solution to be accepted");
             EWOMS_REGISTER_PARAM(TypeTag, double, IluRelaxation, "The relaxation factor of the linear solver's ILU preconditioner");
             EWOMS_REGISTER_PARAM(TypeTag, int, LinearSolverMaxIter, "The maximum number of iterations of the linear solver");
             EWOMS_REGISTER_PARAM(TypeTag, int, LinearSolverRestart, "The number of iterations after which GMRES is restarted");
@@ -299,6 +313,7 @@ namespace Opm
         {
             newton_use_gmres_        = false;
             linear_solver_reduction_ = 1e-2;
+            relaxed_linear_solver_reduction_ = 1e-2;
             linear_solver_maxiter_   = 150;
             linear_solver_restart_   = 40;
             linear_solver_verbosity_ = 0;
diff --git a/opm/simulators/linalg/ISTLSolverEbos.hpp b/opm/simulators/linalg/ISTLSolverEbos.hpp
index 753903ddd..a91464dae 100644
--- a/opm/simulators/linalg/ISTLSolverEbos.hpp
+++ b/opm/simulators/linalg/ISTLSolverEbos.hpp
@@ -434,9 +434,17 @@ std::unique_ptr<Matrix> blockJacobiAdjacency(const Grid& grid,
             // store number of iterations
             iterations_ = result.iterations;
             converged_ = result.converged;
-
+            if(!converged_){
+                if(result.reduction < parameters_.relaxed_linear_solver_reduction_){
+                    std::stringstream ss;
+                    ss<< "Full linear solver tolerance not achived. The reduction is:" << result.reduction
+                      << " after " << result.iterations << " iterations ";
+                    OpmLog::warning(ss.str());
+                    converged_ = true;
+                }
+            }
             // Check for failure of linear solver.
-            if (!parameters_.ignoreConvergenceFailure_ && !result.converged) {
+            if (!parameters_.ignoreConvergenceFailure_ && !converged_) {
                 const std::string msg("Convergence failure for linear solver.");
                 OPM_THROW_NOLOG(NumericalProblem, msg);
             }