A corrected XFEM approximation without problems in blending elements

Thomas Peter Fries*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The extended finite element method (XFEM) enables local enrichments of approximation spaces. Standard finite elements are used in the major part of the domain and enriched elements are employed where special solution properties such as discontinuities and singularities shall be captured. In elements that blend the enriched areas with the rest of the domain problems arise in general. These blending elements often require a special treatment in order to avoid a decrease in the overall convergence rate. A modification of the XFEM approximation is proposed in this work. The enrichment functions are modified such that they are zero in the standard elements, unchanged in the elements with all their nodes being enriched, and varying continuously in the blending elements. All nodes in the blending elements are enriched. The modified enrichment function can be reproduced exactly everywhere in the domain and no problems arise in the blending elements. The corrected XFEM is applied to problems in linear elasticity and optimal convergence rates are achieved.

Original languageEnglish
Pages (from-to)503-532
Number of pages30
JournalInternational Journal for Numerical Methods in Engineering
Issue number5
Publication statusPublished - 30 Jul 2008


  • Corrected XFEM
  • Modified enrichment
  • Optimal convergence
  • XFEM

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Computational Mechanics
  • Applied Mathematics


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