Robust residual-based a posteriori Arnold-Winther mixed finite element analysis in elasticity

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• 作者：Carsten Carstensen^a ; ^{cc@mathematik.hu-berlin.de" class="auth_mail" title="E-mail the corresponding author} ; Joscha Gedicke^b ; ^{joscha.gedicke@iwr.uni-heidelberg.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Finite element method ; Arnold&ndash ; Winther ; A posteriori error analysis ; Robustness ; Elasticity
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：300
• 期：Complete
• 页码：245-264
• 全文大小：432 K

文摘

This paper presents a residual-based a posteriori error estimator for the Arnold–Winther mixed finite element that utilises a post-processing for the skew-symmetric part of the strain. Numerical experiments verify the proven reliability and efficiency for suitable approximation of the skew-symmetric deformation gradient. Numerical evidence supports that the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0045782515003205&_mathId=si2.gif&_user=111111111&_pii=S0045782515003205&_rdoc=1&_issn=00457825&md5=76f7321a15fa879194a55089ae7e8a75" title="Click to view the MathML source">L²class="mathContainer hidden">class="mathCode">$L^2$-stress error estimator is robust in the Poisson ratio and allows stable error control even in the incompressible limit.