Reference : A simple error estimator for extended finite elements
Scientific journals : Article
Engineering, computing & technology : Multidisciplinary, general & others
Computational Sciences
A simple error estimator for extended finite elements
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Duflot, Marc [CENAERO, Avenue Jean Mermoz 30, B-6041 Gosselies, Belgium]
Le, Phong [Computational Engineering Research Centre, Faculty of Engineering and Surveying, University of Southern Queensland]
Communications in Numerical Methods in Engineering
Yes (verified by ORBilu)
[en] A posteriori error estimation ; Derivative recovery ; Extended finite element method ; Intrinsic enrichment ; Moving least-squares approximation ; Near-tip enrichment ; Computational fluid dynamics ; Error analysis ; Fracture mechanics ; Least squares approximations ; Polynomial approximation ; Strain ; Strength of materials ; Finite element method
[en] 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.
FEDER European funds under contract No. EP1A122030000102

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