Overview and comparison of different variants of the XFEM

Publikation: Beitrag in einer FachzeitschriftKonferenzartikel

Abstract

Different variants of the eXtended Finite Element Method (XFEM) have developed over the last years: The original, shifted, corrected, stable, and intrinsic XFEM. Herein, these variants are compared in terms of convergence rates and conditioning of the resulting systems of equations. Optimal convergence rates are achieved by the corrected, stable, and intrinsic XFEM for general enrichments. The original and shifted XFEM achieve optimal rates for selected enrichments only. In terms of the conditioning, it is found that the stable XFEM can be “optimal” in the sense that the same dependency on the mesh size as for the classical FEM is maintained. However, this finding only holds if one enrichment term is involved. In the presence of several enrichment terms, only the intrinsic XFEM yields well-conditioned systems of equations
Originalspracheenglisch
Seiten (von - bis)27-30
FachzeitschriftProceedings in Applied Mathematics and Mechanics
Jahrgang14
Ausgabenummer1
DOIs
PublikationsstatusVeröffentlicht - 2014
Veranstaltung85th Annual Meeting of the International Association of Applied Mathematics and Mechanics: GAMM 2014 - Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Deutschland
Dauer: 10 März 201414 März 2014

Fields of Expertise

  • Advanced Materials Science

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

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