A rectangular mixed element method with continuous flux approximation for coupling Stokes and Darcy flows

We construct and analyze herein a mixed element method with continuous flux approximation based on staggered rectangular meshes for solving the model of Stokes equation coupled with Darcy equation with Beavers–Joseph–Saffman interface condition. We prove the inf–sup condition and the approximate solution existence uniquely. The L2L2 error estimates are established for both the velocity and pressure. Numerical experiments are given to verify the convergence rate for the problem.