A two-grid decoupled penalty finite element method for the stationary Stokes–Darcy problem

In this paper, a two-grid decoupled penalty finite element method has been constructed for solving the mixed Stokes–Darcy model. We first introduce a penalty Stokes–Darcy model based on the penalty method at the continuous level and then show its solution converges to the original one as Oϵ where the penalty parameter is ϵ→0. Then a two-grid method is used to decouple the penalty model. On the coarse mesh, it requires to solve the penalty model. On the fine mesh, we only need to solve two independent subproblems, while we avoid solving a saddle point problem in the fluid region due to the penalty method. We also provide the error estimates in which we prove the optimal convergence order with h=H². In the final, we perform the numerical tests which indicate that our proposed scheme is effective and can achieve the same accuracy as the directly coupled finite element method.