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

Fingerprint

Generalized Finite Element Method
Extended Finite Element Method
Finite element method
Shear Bands
Polynomial approximation
Approximation Space
Shear bands
Kink
Solidification
Polynomial Approximation
Dislocation
Crack
Jump
Finite Element Method
Singularity
Cracks
Approximation
Simulation

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

Cite this

The extended/generalized finite element method : An overview of the method and its applications. / Fries, Thomas Peter; Belytschko, Ted.

In: International journal for numerical methods in engineering, Vol. 84, No. 3, 15.10.2010, p. 253-304.

Research output: Contribution to journalArticleResearchpeer-review

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