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

Octavio Andrés González‐Estrada ((Authors' affiliations are shown at the end of the article.))
Juan José Ródenas ((Authors' affiliations are shown at the end of the article.))
Stéphane Pierre Alain Bordas ((Authors' affiliations are shown at the end of the article.))
Marc Duflot ((Authors' affiliations are shown at the end of the article.))
Pierre Kerfriden ((Authors' affiliations are shown at the end of the article.))
Eugenio Giner ((Authors' affiliations are shown at the end of the article.))

Engineering Computations

ISSN: 0264-4401

Publication date: 9 November 2012

Abstract

Purpose

The purpose of this paper is to assess the effect of the statical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also 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

The authors 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

The paper shows that both extended recovery procedures and statical admissibility are key to an accurate assessment of the quality of enriched finite element approximations.

Keywords

Citation

Andrés González‐Estrada, O., José Ródenas, J., Pierre Alain Bordas, S., Duflot, M., Kerfriden, P. and Giner, E. (2012), "On the role of enrichment and statical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods", Engineering Computations, Vol. 29 No. 8, pp. 814-841. https://doi.org/10.1108/02644401211271609

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Publisher

:

Emerald Group Publishing Limited

Copyright © 2012, Emerald Group Publishing Limited

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