Math. Model. Nat. Phenom.
Volume 4, Number 1, 2009Modelling and numerical methods in contact mechanics
|Page(s)||88 - 105|
|Published online||27 January 2009|
A Reduced Basis Enrichment for the eXtended Finite Element Method
Institut de Mathématiques, UMR CNRS 5215, GMM INSA Toulouse,
Complexe scientifique de Rangueil, 31077 Toulouse Cedex 4, France
2 Institut de Mathématiques, UMR CNRS 5215, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France
3 Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, F-69621, Villeurbanne, France
Corresponding author: Yves.Renard@insa-lyon.fr
This paper is devoted to the introduction of a new variant of the extended finite element method (Xfem) for the approximation of elastostatic fracture problems. This variant consists in a reduced basis strategy for the definition of the crack tip enrichment. It is particularly adapted when the asymptotic crack-tip displacement is complex or even unknown. We give a mathematical result of quasi-optimal a priori error estimate and some computational tests including a comparison with some other strategies.
Mathematics Subject Classification: 74R99 / 74S05 / 65N30
Key words: fracture / finite element method / Xfem / reduced basis / error estimates
© EDP Sciences, 2009
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