The extended/generalized finite element method: An overview of the method and its applications

Thomas Peter Fries, Ted Belytschko

Research output: Contribution to journalArticleResearchpeer-review

Abstract

An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non-smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi-field problems.

Original languageEnglish
Pages (from-to)253-304
Number of pages52
JournalInternational journal for numerical methods in engineering
Volume84
Issue number3
DOIs
Publication statusPublished - 15 Oct 2010

Keywords

  • Extended finite element method
  • Generalized finite element method
  • GFEM
  • Partition of unity method
  • PUM
  • Review
  • XFEM

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics
  • Numerical Analysis

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