A strongly conservative finite element method for the coupling of Stokes and Darcy flow

We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers–Joseph–Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in Hdiv(Ω) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders.