Expandable Local and Parallel Two-Grid Finite Element Scheme for the Stokes Equations
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In this paper, we present a novel local and parallel two-grid finite element scheme for solving the Stokes equations, and rigorously establish its a priori error estimates. The scheme admits simultaneously small scales of subproblems and distances between subdomains and its expansions, and hence can be expandable. Based on the a priori error estimates, we provide a corresponding iterative scheme with suitable iteration number. The resulting iterative scheme can reach the optimal convergence orders within specific two-grid iterations (O(|ln H|^2) in 2-D and O(|ln H|) in 3-D) if the coarse mesh size H and the fine mesh size h are properly chosen. Finally, some numerical tests including 2-D and 3-D cases are carried out to verify our theoretical results.
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