We consider the flow of a viscous incompressible fluid in a rigid homogeneous porousmedium provided with mixed boundary conditions. Since the boundary pressure can presenthigh variations, the permeability of the medium also depends on the pressure, so that themodel is nonlinear. A posteriori estimates allow us to omit thisdependence where the pressure does not vary too much. We perform the numerical analysis ofa spectral element discretization of the simplified model. Finally we propose a strategywhich leads to an automatic identification of the part of the domain where the simplifiedmodel can be used without increasing significantly the error.
