TY  - JOUR
AB  - 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.
VL  - 29
IS  - 8
SN  - 0264-4401
DO  - 10.1108/02644401211271609
UR  - https://doi.org/10.1108/02644401211271609
AU  - Andrés González‐Estrada Octavio
AU  - José Ródenas Juan
AU  - Pierre Alain Bordas Stéphane
AU  - Duflot Marc
AU  - Kerfriden Pierre
AU  - Giner Eugenio
PY  - 2012
Y1  - 2012/01/01
TI  - On the role of enrichment and statical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods
T2  - Engineering Computations
PB  - Emerald Group Publishing Limited
SP  - 814
EP  - 841
Y2  - 2024/05/08
ER  -