A simple error estimator for extended finite elements

Article


Bordas, Stephane, Duflot, Marc and Le, Phong. 2008. "A simple error estimator for extended finite elements." Communications in Numerical Methods in Engineering. 24 (11), pp. 961-971. https://doi.org/10.1002/cnm.1001
Article Title

A simple error estimator for extended finite elements

ERA Journal ID490
Article CategoryArticle
AuthorsBordas, Stephane (Author), Duflot, Marc (Author) and Le, Phong (Author)
Journal TitleCommunications in Numerical Methods in Engineering
International Journal for Numerical Methods in Biomedical Engineering
Journal Citation24 (11), pp. 961-971
Number of Pages11
Year2008
Place of PublicationBognor Regis, West Sussex, United Kingdom
ISSN2040-7939
2040-7947
Digital Object Identifier (DOI)https://doi.org/10.1002/cnm.1001
Web Address (URL)http://onlinelibrary.wiley.com/doi/10.1002/cnm.1001/pdf
Abstract

This short communication presents the idea of an a posteriori error estimate for enriched (extended) finite elements (XFEM). The enhanced strain field against which the XFEM strains are compared, is computed through extended moving least-squares smoothing constructed using the diffraction method to preserve the discontinuity. The error estimator is the L2 norm of the difference of the XFEM strain with the enhanced strain. We prove the concept of the proposed method on a 1D example with a singular solution and a 2D fracture mechanics example and conclude with some future work based on our paradigm.

Keywordsa posteriori error estimation; derivative recovery; extended finite element method; intrinsic enrichment; moving least-squares approximation; near-tip enrichment
ANZSRC Field of Research 2020490302. Numerical analysis
490109. Theoretical and applied mechanics
401706. Numerical modelling and mechanical characterisation
Public Notes

Journal name change in 2010 to : International Journal for Numerical Methods in Biomedical Engineering. Permanent restricted access to published version due to publisher copyright policy.

Byline AffiliationsUniversity of Glasgow, United Kingdom
Cenaero, Belgium
Computational Engineering and Science Research Centre
Institution of OriginUniversity of Southern Queensland
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