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A Reduced Basis Enrichment for the eXtendedFinite Element Method

Published online by Cambridge University Press:  27 January 2009

E. Chahine,
P. Laborde and
Y. Renard
E. Chahine
Affiliation:
Institut de Mathématiques, UMR CNRS 5215, GMM INSA Toulouse, Complexe scientifique de Rangueil, 31077 Toulouse Cedex 4, France
P. Laborde
Affiliation:
Institut de Mathématiques, UMR CNRS 5215, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France
Y. Renard*
Affiliation:
Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, F-69621, Villeurbanne, France
*
Yves.Renard@insa-lyon.fr
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Abstract

This paper is devoted to the introduction of a new variant of the extendedfinite element method (Xfem) for the approximation of elastostatic fractureproblems. This variant consists in a reduced basis strategy for the definitionof the crack tip enrichment. It is particularly adapted when the asymptoticcrack-tip displacement is complex or even unknown. We give a mathematical resultof quasi-optimal a priori error estimate and some computational tests includinga comparison with some other strategies.

Keywords

fracturefinite element methodXfemreduced basiserrorestimates

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