The intrinsic XFEM: A method for arbitrary discontinuities without additional unknowns

Thomas Peter Fries*, Ted Belytschko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A new method for treating arbitrary discontinuities in a finite element (FE) context is presented. Unlike the standard extended FE method (XFEM), no additional unknowns are introduced at the nodes whose supports are crossed by discontinuities. The method constructs an approximation space consisting of mesh-based, enriched moving least-squares (MLS) functions near discontinuities and standard FE shape functions elsewhere. There is only one shape function per node, and these functions are able to represent known characteristics of the solution such as discontinuities, singularities, etc. The MLS method constructs shape functions based on an intrinsic basis by minimizing a weighted error functional. Thereby, weight functions are involved, and special mesh-based weight functions are proposed in this work. The enrichment is achieved through the intrinsic basis. The method is illustrated for linear elastic examples involving strong and weak discontinuities, and matches optimal rates of convergence even for crack-tip applications.

Original languageEnglish
Pages (from-to)1358-1385
Number of pages28
JournalInternational Journal for Numerical Methods in Engineering
Issue number13
Publication statusPublished - 24 Dec 2006


  • Cracks
  • Discontinuities
  • MLS
  • XFEM

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Applied Mathematics
  • Computational Mechanics

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