A corrected XFEM approximation without problems in blending elements

• Published in: International journal for numerical methods in engineering Vol. 75; no. 5; pp. 503 - 532
• Main Author: Fries, Thomas-Peter
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 30.07.2008; Wiley
• Subjects: Computational techniques; corrected XFEM; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; modified enrichment; optimal convergence; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; XFEM; Finite element method; Discontinuity; Singularity; Linear elasticity; optimal convergence; modified enrichment; Convergence rate; corrected XFEM; Modeling; Numerical convergence; eXtended Finite Element Method; XFEM
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.2259

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. Copyright © 2007 John Wiley & Sons, Ltd.