A conforming mixed flnite element method for the coupling of fluid flow with porous media flow

Abstract

We consider a porous media entirely enclosed within a fluid region, and present a well posed conforming mixed flnite element method for the corresponding coupled problem. The interface conditions refer to mass conservation, balance of normal forces, and the Beavers-Joseph-Safiman law, which yields the introduction of the trace of the porous media pressure as a suitable Lagrange multiplier. The flnite element subspaces deflning the discrete formulation employ Bernardi-Raugel and Raviart-Thomas elements for the velocities, piecewise constants for the pressures, and continuous piecewise linear elements for the Lagrange multiplier. We show stability, convergence, and a priori error estimates for the associated Galerkin scheme. Finally, we provide several numerical results illustrating the good performance of the method and conflrming the theoretical rates of convergence.