Finite element methods for coupling surface flow with porous media flow

A unified finite element stabilization approach, for the simulation of coupled surface flow withporous media flow, is investigated. The success of symmetric stabilization such as local projection and subgrid methods; inherited from solving steady state Stokes like problems is extended to the coupling of surface and porous media flow problems. Existence and uniqueness results of a weak solution and numerical scheme are investigated. In this work we will derive a priori error estimates for the numerical scheme. Also, we consider the approach that decouples the problem naturally into two problems, one in the free flow domain and other in the porous medium.