Coupling Stokes and Darcy equations

We study an interface problem between a fluid flow, governed by Stokes equations, and a flow in a porous medium, governed by Darcy equations. We consider a weak formulation of the coupled problem which allows to use classical Stokes finite elements in the fluid domain, and standard continuous piecewise polynomials in the porous medium domain. Meshes do not need to match at the interface. The formulation of Stokes equations is standard while a Galerkin least-squares formulation is used for a mixed form of Darcy equations. We prove the well-posedness of the coupled problem for this formulation and the convergence for some finite element approximations. A two-dimensional numerical example is also given.