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 pan id="mmlsi1" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_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)pan>pan class="mathContainer hidden">pan class="mathCode"><math altimg="si1.gif" overflow="scroll">mathvariant="script">O(Δt+h)math>pan>pan>pan> for the velocity and the magnetic field in the discrete space pan id="mmlsi2" class="mathmlsrc">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">lineImage" height="17" width="102" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716304253-si2.gif">pan class="mathContainer hidden">pan class="mathCode"><math altimg="si2.gif" overflow="scroll">l2(mathvariant="bold">H1)∩l∞(mathvariant="bold">L2)math>pan>pan>pan> under the constraint pan id="mmlsi3" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_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≥Chpan>pan class="mathContainer hidden">pan class="mathCode"><math altimg="si3.gif" overflow="scroll">Δt≥Chmath>pan>pan>pan>.