zbMATH — the first resource for mathematics

A conforming mixed finite element method for the coupling of fluid flow with porous media flow. (English) Zbl 1157.76025
Summary: We consider a porous medium entirely enclosed within a fluid region and present a well-posed conforming mixed finite element method for the corresponding coupled problem. The interface conditions refer to mass conservation, balance of normal forces and the Beavers-Joseph-Saffman law, which yields the introduction of the trace of the porous medium pressure as a suitable Lagrange multiplier. The finite element subspaces defining 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 prove 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 confirming the theoretical rates of convergence.

76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
76D07 Stokes and related (Oseen, etc.) flows
Full Text: DOI