A modified local and parallel finite element method for the mixed Stokes–Darcy model

Based on two-grid discretizations, a modified local and parallel finite element algorithm for the mixed Stokes–Darcy problem is proposed and analyzed in this paper. The idea is that, on the coarse grid, we solve a coupled Stokes–Darcy problem; on the fine grid, we first consider the discrete Darcy problem with a coarse grid approximation uHuH to the interface coupling conditions, then solve a series of independent local Stokes subproblems with the numerical solution of Darcy problem on fine grid to the interface coupling conditions in parallel. Optimal error estimates are obtained, and numerical experiments demonstrate the accuracy and efficiency of the modified local and parallel algorithm.