Two‐level stabilized finite volume method for the stationary incompressible magnetohydrodynamic equations
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Published:2023-05-20
Issue:6
Volume:39
Page:4196-4220
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ISSN:0749-159X
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Container-title:Numerical Methods for Partial Differential Equations
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language:en
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Short-container-title:Numerical Methods Partial
Author:
Chu Xiaochen1,
Chen Chuanjun1ORCID,
Zhang Tong1ORCID
Affiliation:
1. School of Mathematics and Information Sciences Yantai University Yantai China
Abstract
AbstractIn this paper, a two‐level stabilized finite volume method is developed and analyzed for the steady incompressible magnetohydrodynamic (MHD) equations. The linear polynomial space is used to approximate the velocity, pressure and magnetic fields, and two local Gauss integrations are introduced to overcome the restriction of discrete inf‐sup condition. Firstly, the existence and uniqueness of the solution of the discrete problem in the stabilized finite volume method are proved by using the Brouwer's fixed point theorem. ‐stability results of numerical solutions are also presented. Secondly, optimal error estimates of numerical solutions in and ‐norms are established by using the energy method and constructing the corresponding dual problem. Thirdly, the stability and convergence of two‐level stabilized finite volume method for the stationary incompressible MHD equations are provided. Theoretical findings show that the two‐level method has the same accuracy as the one‐level method with the mesh sizes . Finally, some numerical results are provided to identify with the established theoretical findings and show the performances of the considered numerical schemes.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Henan Province
Natural Science Foundation of Shandong Province
Subject
Applied Mathematics,Computational Mathematics,Numerical Analysis,Analysis