Error analysis of a fractional-step method for magnetohydrodynamics equations

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• 作者：Rong An ; ^{anrong702@aliyun.com" class="auth_mail" title="E-mail the corresponding author} ; ^{anrong702@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Can Zhou
• 关键词：65M12 ; 76W05
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：168-184
• 全文大小：483 K

文摘

This paper focuses on a fractional-step finite element method for the magnetohydrodynamics problems in three-dimensional bounded domains. It is shown that the proposed fractional-step scheme allows for a discrete energy identity. A rigorous error analysis is presented. We derive the temporal and spatial error estimates of O(Δt+h)$\mathcal{O}(\Delta t+h)$ for the velocity and the magnetic field in the discrete space $l^2\left(H^1\right)\cap l^{\infty }\left(L^2\right)$ under the constraint Δt≥Ch$\Delta t\ge Ch$.