Equilibrated stress reconstructions for linear elasticity problems with application to a posteriori error analysisReport as inadecuate




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1 IMAG - Institut Montpelliérain Alexander Grothendieck 2 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles 3 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique

Abstract : We present an a posteriori error estimate for the linear elasticity problem. The estimate is based on an equilibrated reconstruction of the Cauchy stress tensor, which is obtained from mixed finite element solutions of local Neumann problems. We propose two different reconstructions, one using Arnold–Winther mixed finite element spaces providing a symmetric stress tensor and one using Arnold–Falk– Winther mixed finite element spaces with a weak symmetry constraint. The performance of the estimate is illustrated on a numerical test with analytical solution.

Keywords : equilibrated stress reconstruction a posteriori error estimate linear elasticity Arnold–Winther finite element Arnold–Falk–Winther finite element





Author: Rita Riedlbeck - Daniele Di Pietro - Alexandre Ern -

Source: https://hal.archives-ouvertes.fr/



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