A unified mixed formulation naturally coupling Stokes and Darcy flows

Abstract

Solving Stokes–Darcy coupled flow using stable Galerkin formulations for both subproblems usually leads to unbalanced rates of convergence. We present a stabilized mixed finite element method for Darcy flow, compatible with Galerkin stable elements for the Stokes problem, with balanced rates of convergence in H 1 norm for velocity and L 2 for pressure. The discontinuities of the solutions on the interface of the free-fluid and the porous medium are incorporated in the finite element approximation by simple linear transformations derived from the interface conditions. The resulting global finite element system can be assembled and directly solved using standard finite element implementation. Results of some numerical experiments are presented to demonstrate the flexibility and the robustness of the proposed finite element formulation.