diff --git a/dune/mmdg/problems/mmdgproblem2.hh b/dune/mmdg/problems/mmdgproblem2.hh
index 79e0595949344b4eec38962dfde54421fce1f3c8..24610882dbb644752546693d1324c263720d2ed0 100644
--- a/dune/mmdg/problems/mmdgproblem2.hh
+++ b/dune/mmdg/problems/mmdgproblem2.hh
@@ -11,6 +11,8 @@ class MMDGProblem2 : public CoupledDGProblem<Coordinate, Scalar>
 {
   public:
     static constexpr int dim = Coordinate::dimension;
+    using Base = CoupledDGProblem<Coordinate, Scalar>;
+    using Matrix = typename Base::Matrix;
 
     //the exact bulk solution at position pos
     Scalar exactSolution (const Coordinate& pos) const
@@ -25,7 +27,7 @@ class MMDGProblem2 : public CoupledDGProblem<Coordinate, Scalar>
     {
       constexpr Scalar cos2 = std::cos(2.0);
       constexpr Scalar sin2 = std::sin(2.0);
-      return 0.75 * (cos2 - sin2) * std::cos(M_PI * pos[1]);
+      return 0.75 * (cos2 + sin2) * std::cos(M_PI * pos[1]);
     }
 
     //indicates whether an exact solution is implemented for the problem
@@ -57,6 +59,20 @@ class MMDGProblem2 : public CoupledDGProblem<Coordinate, Scalar>
       return Scalar(0.25);
     }
 
+    //tangential permeability tensor per aperture of the interface
+    //at position pos
+    Matrix Kparallel (const Coordinate& pos) const
+    {
+      return Base::Kparallel(pos) / aperture(pos);
+    }
+
+    //permeability of the fracture per aperture in normal direction
+    //at position pos
+    virtual Scalar Kperp (const Coordinate& pos) const
+    {
+      return Scalar(2.0);
+    }
+
     //returns the recommended quadrature order to compute an integral
     //over x * q(x)
     int quadratureOrder_q () const