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

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Abstract

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 uH 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.

Keywords

Stokes equations
Darcy's law
Decoupling
Two-grid algorithm
Parallel finite element method

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Subsidized by NSFC (Grant No. 11571274 & 11171269) and the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20110201110027).