Optimal convergence analysis for the extended finite element method

Authors

  • Serge Nicaise,

    1. Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, Institut des Sciences et Techniques de Valenciennes, F-59313, Valenciennes Cedex 9, France
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  • Yves Renard,

    Corresponding author
    1. Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, F-69621, Villeurbanne, France
    • Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, F-69621, Villeurbanne, France
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  • Elie Chahine

    1. Laboratory for Nuclear Materials, Nuclear Energy and Safety Research Department, Paul Scherrer Institute OVGA/14, CH-5232 Villigen PSI, Switzerland
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Abstract

We establish some optimal a priori error estimates on some variants of the eXtended Finite Element Method (Xfem), namely the Xfem with a cut-off function and the standard Xfem with a fixed enrichment area. Both the Lamé system (homogeneous isotropic elasticity) and the Laplace problem are considered. The convergence of the numerical stress intensity factors is also investigated. Some numerical experiments corroborating the theoretical results are presented. Copyright © 2011 John Wiley & Sons, Ltd.

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