On the role of enrichment and statical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods

Gonzalez Estrada, Octavio Andres, Ródenas, Juan José, Bordas, Stephane Pierre Alain ORCID: https://orcid.org/0000-0001-8634-7002, Duflot, Marc, Kerfriden, Pierre ORCID: https://orcid.org/0000-0002-7749-3996 and Giner, Eugenio 2012. On the role of enrichment and statical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods. Engineering Computations 29 (8) , pp. 814-841. 10.1108/02644401211271609

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Abstract

Purpose – This paper aims at assessing the effect of (1) the statical admissibility of the recovered solution; (2) the ability of the recovered solution to represent the singular solution; on the accuracy, local and global effectivity of recovery-based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM). Design/methodology/approach – We study the performance of two recovery techniques. The first is a recently developed superconvergent patch recovery procedure with equilibration and enrichment (SPR-CX). The second is known as the extended moving least squares recovery (XMLS), which enriches the recovered solutions but does not enforce equilibrium constraints. Both are extended recovery techniques as the polynomial basis used in the recovery process is enriched with singular terms for a better description of the singular nature of the solution. Findings – Numerical results comparing the convergence and the effectivity index of both techniques with those obtained without the enrichment enhancement clearly show the need for the use of extended recovery techniques in Zienkiewicz-Zhu type error estimators for this class of problems. The results also reveal significant improvements in the effectivities yielded by statically admissible recovered solutions. Originality/value – This work shows that both extended recovery procedures and statical admissibility are key to an accurate assessment of the quality of enriched finite element approximations.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Advanced Research Computing @ Cardiff (ARCCA) Engineering
Subjects:	T Technology > TJ Mechanical engineering and machinery
Uncontrolled Keywords:	extended finite element method ; error estimation ; linear elastic fracture mechanics ; statical admissibility ; extended recovery
Publisher:	Emerald
ISSN:	0264-4401
Last Modified:	11 Mar 2023 02:12
URI:	https://orca.cardiff.ac.uk/id/eprint/37235

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