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Local and parallel finite element algorithm for stationary incompressible magnetohydrodynamics
Author(s) -
Zhang Yuhong,
Hou Yanren,
Shan Li,
Dong Xiaojing
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22151
Subject(s) - discretization , mathematics , finite element method , compressibility , grid , a priori and a posteriori , partial differential equation , nonlinear system , series (stratigraphy) , algorithm , mathematical optimization , mathematical analysis , geometry , physics , mechanics , paleontology , philosophy , epistemology , quantum mechanics , biology , thermodynamics
This article presents a local and parallel finite element method for the stationary incompressible magnetohydrodynamics problem. The key idea of this algorithm comes from the two‐grid discretization technique. Specifically, we solve the nonlinear system on a global coarse mesh, and then solve a series of linear problems on several subdomains in parallel. Furthermore, local a priori estimates are obtained on a general shape regular grid. The efficiency of the algorithm is also illustrated by some numerical experiments.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1513–1539, 2017