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 L 2 error estimates are established for both the velocity and pressure. Numerical experiments are given to verify the convergence rate for the problem.

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