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

"This article is (c) Emerald Group Publishing and permission has been granted for this version to appear here (please insert the web address here). Emerald does not grant permission for this article to be further copied/distributed or hosted elsewhere without the express permission from Emerald Group Publishing Limited."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.Stéphane Bordas would like to thank the Royal Academy of Engineering and of the Leverhulme Trust for supporting his Senior Research Fellowship entitled “Towards the next generation surgical simulators” as well as the EPSRC for support under grant EP/G042705/1 Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method.This work has been carried out within the framework of the research projects DPI2007‐66773‐C02‐01, DPI2010‐20542 and DPI2010‐20990 of the Ministerio de Ciencia e Innovacion (Spain). Funding from Feder, Universitat Politecnica de Valencia and Generalitat Valenciana is also acknowledged.González Estrada, OA.; Ródenas, J.; Bordas, SPA.; Duflot, M.; Kerfriden, P.; Giner Maravilla, E. (2012). 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