Optimal convergence analysis for the extended finite element method

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...

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Veröffentlicht in:	International journal for numerical methods in engineering 2011-04, Vol.86 (4-5), p.528-548
Hauptverfasser:	Nicaise, Serge, Renard, Yves, Chahine, Elie
Format:	Artikel
Sprache:	eng
Schlagworte:	Convergence Copyrights Engineering Sciences error estimates Estimates Exact sciences and technology extended finite element method Finite element method Fracture mechanics (crack, fatigue, damage...) Fundamental areas of phenomenology (including applications) Mathematical analysis Mathematics Mechanics Numerical Analysis Optimization Physics Solid mechanics Static elasticity (thermoelasticity...) stress intensity factors Structural and continuum mechanics Structural mechanics Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Beschreibung
Zusammenfassung:	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.
ISSN:	0029-5981 1097-0207 1097-0207
DOI:	10.1002/nme.3092