Geodesic
A Reduced Basis Enrichment for the eXtended Finite Element Method
E. Chahine1 ; P. Laborde2 ; Y. Renard3
1 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
Mathematical modelling of natural phenomena, Tome 4 (2009) no. 1, pp. 88-105.

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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.
DOI : 10.1051/mmnp/20094104

E. Chahine 1 ; P. Laborde 2 ; Y. Renard 3

1 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 
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E. Chahine; P. Laborde; Y. Renard. A Reduced Basis Enrichment for the eXtended Finite Element Method. Mathematical modelling of natural phenomena, Tome 4 (2009) no. 1, pp. 88-105. doi : 10.1051/mmnp/20094104. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20094104/

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