The permeability tensor is computed averages the velocities of those cell solutions. In our case, the cell is symmetric, thus the permeability tensor is isotropic and determined by a scalar K.
We have solved this problem using mixed (Q5)2/Q4 finite elements. Linear solver was a W(1,1)-multigrid cycle with a vertex-centered subspace correction scheme as smoother. Convergence rates were generally smaller than 0.05.
The history of this calculation was as follows: