Convergence Analysis of Some Finite Element Parallel Algorithms for the Stationary Incompressible MHD Equations
Year: 2024
Author: Xiaojing Dong, Yinnian He
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 49–70
Abstract
By combination of iteration methods with the partition of unity method (PUM), some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics (MHD) with different physical parameters are presented and analyzed. These algorithms are highly efficient. At first, a global solution is obtained on a coarse grid for all approaches by one of the iteration methods. By parallelized residual schemes, local corrected solutions are calculated on finer meshes with overlapping sub-domains. The subdomains can be achieved flexibly by a class of PUM. The proposed algorithm is proved to be uniformly stable and convergent. Finally, one numerical example is presented to confirm the theoretical findings.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2201-m2021-0140
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 1 : pp. 49–70
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Partition of unity method Local and parallel algorithm Finite element method Iteration methods Magnetohydrodynamics.