2020/12/07 by Yanren Hou, Feng Shi, Hou, Yanren +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2012.04097
arxiv created 2020/12/07 · openalex publication_date 2020/12/07 · arxiv updated 2020/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.