TY - JOUR
T1 - On the role of enrichment and statistical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods
AU - González-Estrada, Octavio Andres
AU - Ródenas, Juan José
AU - Bordas, Stéphane Pierre Alain
AU - Duflot, Marc
AU - Kerfriden, Pierre
AU - Giner, Eugenio
PY - 2012
Y1 - 2012
N2 - Purpose - The purpose of this paper is to assess the effect of the statistical 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 statistically admissible recovered solutions. Originality/value - The paper shows that both extended recovery procedures and statistical admissibility are key to an accurate assessment of the quality of enriched finite element approximations.
AB - Purpose - The purpose of this paper is to assess the effect of the statistical 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 statistically admissible recovered solutions. Originality/value - The paper shows that both extended recovery procedures and statistical admissibility are key to an accurate assessment of the quality of enriched finite element approximations.
KW - Error analysis
KW - Error estimation
KW - Extended finite element method
KW - Extended recovery
KW - Finite element analysis
KW - Linear elastic fracture mechanics
KW - Statistical admissibility
UR - http://www.scopus.com/inward/record.url?scp=84868563864&partnerID=8YFLogxK
U2 - 10.1108/02644401211271609
DO - 10.1108/02644401211271609
M3 - Article
AN - SCOPUS:84868563864
SN - 0264-4401
VL - 29
SP - 814
EP - 841
JO - Engineering Computations (Swansea, Wales)
JF - Engineering Computations (Swansea, Wales)
IS - 8
ER -