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Optimal convergence analysis for the extended finite element method
Author(s) -
Nicaise Serge,
Renard Yves,
Chahine Elie
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3092
Subject(s) - extended finite element method , finite element method , isotropy , convergence (economics) , mathematics , laplace transform , a priori and a posteriori , numerical analysis , homogeneous , elasticity (physics) , mathematical optimization , mathematical analysis , structural engineering , physics , combinatorics , engineering , philosophy , epistemology , quantum mechanics , economics , thermodynamics , economic growth
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.