LAUSR

We consider the coupling of free and porous media flow governed by Stokes and Darcy equations with the Beavers–Joseph–Saffman interface condition. This model is discretized using a divergence-conforming finite element for the velocities in the whole domain. Hybrid discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. The discretization achieves mass conservation in the sense of $$H(\mathrm {div},\Omega )$$H(div,Ω), and we obtain optimal velocity convergence. Numerical results are presented to validate the theoretical findings.