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arXiv · 2012.04097

Expandable Local and Parallel Two-Grid Finite Element Scheme for the Stokes Equations

Yanren Hou·Feng Shi·Haibiao Zheng
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Abstract

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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Yanren Hou, Feng Shi, Haibiao Zheng. 2020-12-07. Expandable Local and Parallel Two-Grid Finite Element Scheme for the Stokes Equations. https://arxiv.org/abs/2012.04097

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