A hybridizable discontinuous Galerkin method for Stokes/Darcy coupling on dissimilar meshes

Abstract

We present and analyze a hybridizable discontinuous Galerkin method for coupling Stokes and Darcy equations, whose domains are discretized by two independent triangulations. This causes nonconformity at the intersection of the subdomains or leaves a gap (unmeshed region) between them. In order to properly couple the two different discretizations and obtain a high-order scheme, we propose suitable transmission conditions based on mass conservation, equilibrium of normal forces and the Beavers–Joseph–Saffman law. Since the meshes do not necessarily coincide, we use the Transfer Path Method to tie them. We establish the well-posedness of the method and provide error estimates where the influences of the nonconformity and the gap are explicit in the constants. Finally, numerical experiments that illustrate the performance of the method are shown.