A Discontinuous Galerkin Method for the Coupled Stokes and Darcy Problem

Abstract

Combining the mixed discontinuous Galerkin method for the Darcy flow and the interior penalty discontinuous Galerkin methods for the Stokes problem, a locally conservative discrete scheme is proposed for numerically solving the coupled Stokes and Darcy problem. We prove the well-posedness of the solution of the proposed numerical scheme by boundedness, K-ellipticity and a discrete inf-sup condition. A priori error estimates, in proper norms are derived, and to verify the theoretical analysis, some numerical experiments are given.