A simple error estimator for extended finite elements

Bordas, Stephane and 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. ISSN 1069-8299


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.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: 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.
Faculty/School / Institute/Centre: Historic - Faculty of Engineering and Surveying - No Department (Up to 30 Jun 2013)
Faculty/School / Institute/Centre: Historic - Faculty of Engineering and Surveying - No Department (Up to 30 Jun 2013)
Date Deposited: 18 Mar 2013 12:08
Last Modified: 18 Mar 2013 23:56
Uncontrolled Keywords: a posteriori error estimation; derivative recovery; extended finite element method; intrinsic enrichment; moving least-squares approximation; near-tip enrichment
Fields of Research (2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490302 Numerical analysis
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490109 Theoretical and applied mechanics
40 ENGINEERING > 4017 Mechanical engineering > 401706 Numerical modelling and mechanical characterisation
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: https://doi.org/10.1002/cnm.1001
URI: http://eprints.usq.edu.au/id/eprint/20849

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