Reference : On the role of enrichment and statistical admissibility of recovered fields in a post...

	Document type :	Scientific journals : Article
	Discipline(s) :	Engineering, computing & technology : Multidisciplinary, general & others
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/12026

Title :	On the role of enrichment and statistical admissibility of recovered fields in a posteriori error estimation for enriched finite element methods
Language :	English
Author, co-author :	González-Estrada, O. A. [Institute of Modelling and Simulation in Mechanics and Materials, Cardiff School of Engineering, Cardiff University, Cardiff, United Kingdom]
	Ródenas, J. J. [Research Center for Vehicle Technology, Department of Mechanical and Materials Engineering, Universitat Politecnica de Valencia, Valencia, Spain]
	Bordas, Stéphane [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
	Duflot, M. [Multiscale Modeling of Materials and Structures, Cenaero, Gosselies, Belgium]
	Kerfriden, P. [Institute of Modelling and Simulation in Mechanics and Materials, Cardiff School of Engineering, Cardiff University, Cardiff, United Kingdom]
	Giner, E. [Institute of Modelling and Simulation in Mechanics and Materials, Cardiff School of Engineering, Cardiff University, Cardiff, United Kingdom]
Publication date :	2012
Journal title :	Engineering Computations
Volume :	29
Issue/season :	8
Pages :	814-841
Peer reviewed :	Yes (verified by ORBilu)
Audience :	International
ISSN :	0264-4401
Keywords :	[en] Error analysis ; Error estimation ; Extended finite element method ; Extended recovery ; Finite element analysis ; Linear elastic fracture mechanics ; Statistical admissibility ; Design/methodology/approach ; Effectivity index ; Enriched finite elements ; Equilibrium constraint ; Moving least squares ; Numerical results ; Polynomial basis ; Posteriori error estimation ; Recovery procedure ; Recovery process ; Recovery-based error estimators ; Singular solutions ; Superconvergent patch recovery ; Type errors ; Brittle fracture ; Estimation ; Finite element method ; Polynomials ; Recovery
Abstract :	[en] 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. © Emerald Group Publishing Limited.
Research centres :	Institute of Mechanics and Advanced Materials. Cardiff University
Funders :	EPSRC EP/G042705/1
Name of the research project :	Increased Reliability for Industrially Relevant Automatic Crack Growth Simulation with the eXtended Finite Element Method
Target :	Researchers ; Professionals ; Students
Permalink :	http://hdl.handle.net/10993/12026
DOI :	10.1108/02644401211271609
Other URL :	http://www.emeraldinsight.com/journals.htm?issn=0264-4401&volume=29&issue=8&articleid=17063380&show=html
Mentions required by the publisher for OA :	Published in Engineering Computations

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