Iterative methods in penalty finite element discretization for the steady MHD equations

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• 作者：Haiyan Su ^{shymath@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xinlong Feng ; ^{fxlmath@xju.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Pengzhan Huang ^{hpzh007@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65N30 ; 76M10
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2016
• 出版时间：1 June 2016
• 年：2016
• 卷：304
• 期：Complete
• 页码：521-545
• 全文大小：1240 K

文摘

This paper characterizes one penalty finite element method for the incompressible MHD equations. The method is an interesting combination of the classic iterative schemes (Stokes, Newton and Oseen iterations) with two different finite element pairs P₁b$P_{1}b$–P₁$P_1$–P₁b$P_{1}b$ and P₁$P_1$–P₀$P_0$–P₁$P_1$. Moreover, the rigorous analysis of stability and error estimate for the proposed methods are given. Finally, the applicability and effectiveness of the presented schemes are illustrated in several numerical experiments.