Finite element discretization of Darcy's equations with pressure dependent porosity
UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. firstname.lastname@example.org
2 CNRS, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France. email@example.com
3 Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA. firstname.lastname@example.org
We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme 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.
Mathematics Subject Classification: 76S05 / 65N30
Key words: Porous media flows / Darcy equations / finite elements
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