On the role of enrichment and statical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods
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
Publisher
:Emerald Group Publishing Limited
Copyright © 2012, Emerald Group Publishing Limited