A Reduced Basis Enrichment for the eXtended Finite Element Method

E. Chahine; P. Laborde; Y. Renard

Mathematical Modelling of Natural Phenomena (2009)

  • Volume: 4, Issue: 1, page 88-105
  • ISSN: 0973-5348

Abstract

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This paper is devoted to the introduction of a new variant of the extended finite element method (Xfem) for the approximation of elastostatic fracture problems. This variant consists in a reduced basis strategy for the definition of the crack tip enrichment. It is particularly adapted when the asymptotic crack-tip displacement is complex or even unknown. We give a mathematical result of quasi-optimal a priori error estimate and some computational tests including a comparison with some other strategies.

How to cite

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Chahine, E., Laborde, P., and Renard, Y.. "A Reduced Basis Enrichment for the eXtended Finite Element Method." Mathematical Modelling of Natural Phenomena 4.1 (2009): 88-105. <http://eudml.org/doc/222353>.

@article{Chahine2009,
abstract = { This paper is devoted to the introduction of a new variant of the extended finite element method (Xfem) for the approximation of elastostatic fracture problems. This variant consists in a reduced basis strategy for the definition of the crack tip enrichment. It is particularly adapted when the asymptotic crack-tip displacement is complex or even unknown. We give a mathematical result of quasi-optimal a priori error estimate and some computational tests including a comparison with some other strategies.},
author = {Chahine, E., Laborde, P., Renard, Y.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {fracture; finite element method; Xfem; reduced basis; error estimates; error estimates},
language = {eng},
month = {1},
number = {1},
pages = {88-105},
publisher = {EDP Sciences},
title = {A Reduced Basis Enrichment for the eXtended Finite Element Method},
url = {http://eudml.org/doc/222353},
volume = {4},
year = {2009},
}

TY - JOUR
AU - Chahine, E.
AU - Laborde, P.
AU - Renard, Y.
TI - A Reduced Basis Enrichment for the eXtended Finite Element Method
JO - Mathematical Modelling of Natural Phenomena
DA - 2009/1//
PB - EDP Sciences
VL - 4
IS - 1
SP - 88
EP - 105
AB - This paper is devoted to the introduction of a new variant of the extended finite element method (Xfem) for the approximation of elastostatic fracture problems. This variant consists in a reduced basis strategy for the definition of the crack tip enrichment. It is particularly adapted when the asymptotic crack-tip displacement is complex or even unknown. We give a mathematical result of quasi-optimal a priori error estimate and some computational tests including a comparison with some other strategies.
LA - eng
KW - fracture; finite element method; Xfem; reduced basis; error estimates; error estimates
UR - http://eudml.org/doc/222353
ER -

References

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