We consider the flow of a viscous incompressible fluid through a rigidhomogeneous porous medium. The permeability of the medium dependson the pressure, so that the model is nonlinear. We propose a finiteelement discretization of this problem and, in the case where thedependence on the pressure is bounded from above and below, we proveits convergence to the solution and propose an algorithm to solvethe discrete system. In the case where the dependenceon the pressure is exponential, we propose a splittingscheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods.
