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

Salim Meddahi ^{We consider a porous medium entirely enclosed within a fluidregion and present a well-posed conforming mixed finite-elementmethod for the corresponding coupled problem. The interfaceconditions refer to mass conservation, balance of normal forcesand the Beavers–Joseph–Saffman law, which yieldsthe introduction of the trace of the porous medium pressureas a suitable Lagrange multiplier. The finite-element subspacesdefining the discrete formulation employ Bernardi–Raugeland Raviart–Thomas elements for the velocities, piecewiseconstants for the pressures and continuous piecewise-linearelements for the Lagrange multiplier. We show stability, convergenceand a priori error estimates for the associated Galerkin scheme.Finally, we provide several numerical results illustrating thegood performance of the method and confirming the theoreticalrates of convergence.}