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 ce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304253&_mathId=si1.gif&_user=111111111&_pii=S0377042716304253&_rdoc=1&_issn=03770427&md5=96388f286456d7f807ffb8330179b08b" title="Click to view the MathML source">O(Δt+h)$\mathcal{O}(\Delta t+h)$ for the velocity and the magnetic field in the discrete space ce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304253&_mathId=si2.gif&_user=111111111&_pii=S0377042716304253&_rdoc=1&_issn=03770427&md5=f9859561a7086822c47dc7e8eae40c0a">ce" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716304253-si2.gif">$l^2\left(H^1\right)\cap l^{\infty }\left(L^2\right)$ under the constraint ce?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716304253&_mathId=si3.gif&_user=111111111&_pii=S0377042716304253&_rdoc=1&_issn=03770427&md5=cd14c9ba9b34d9317acd8efc72a904a0" title="Click to view the MathML source">Δt≥Ch$\Delta t\ge Ch$.