Numerical Analysis
A quasi-optimal convergence result for fracture mechanics with XFEM
Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 527-532.

The aim of this Note is to give a convergence result for a variant of the eXtended Finite Element Method (XFEM) on cracked domains using a cut-off function to localize the singular enrichment area. The difficulty is caused by the discontinuity of the displacement field across the crack, but we prove that a quasi-optimal convergence rate holds in spite of the presence of elements cut by the crack. The global linear convergence rate is obtained by using an enriched linear finite element method.

Le but de cette Note est de donner un résultat de convergence pour une variante de la méthode XFEM (eXtended Finite Element Method) sur un domaine fissuré en utilisant une fonction cut-off pour localiser l'enrichissement par les fonctions singulières. La difficulté est causée par la discontinuité du champ de déplacement à travers la fissure, mais on montre une convergence quasi-optimale malgré la présence d'éléments coupés par la fissure. Le résultat de convergence globale linéaire est obtenu en utilisant une méthode d'éléments finis affines enrichis.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.02.002
Chahine, Elie 1; Laborde, Patrick 2; Renard, Yves 1

1 MIP, CNRS UMR 5640, INSAT, 135, avenue de Rangueil, 31077 Toulouse cedex 4, France
2 MIP, CNRS UMR 5640, UPS Toulouse 3, 118 route de Narbonne, 31062 Toulouse cedex 4, France
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Chahine, Elie; Laborde, Patrick; Renard, Yves. A quasi-optimal convergence result for fracture mechanics with XFEM. Comptes Rendus. Mathématique, Volume 342 (2006) no. 7, pp. 527-532. doi : 10.1016/j.crma.2006.02.002. http://www.numdam.org/articles/10.1016/j.crma.2006.02.002/

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