EDP Sciences Journals List
Home Document
Subscriber Authentication Point
Issue Math. Model. Nat. Phenom.
Volume 4, Number 1, 2009
Modelling and numerical methods in contact mechanics
Page(s) 88 - 105
DOI 10.1051/mmnp/20094104
Published online 27 January 2009

Math. Model. Nat. Phenom. Vol. 4, No. 1, 2009, pp. 88-105
DOI: 10.1051/mmnp/20094104

A Reduced Basis Enrichment for the eXtended Finite Element Method

E. Chahine1, P. Laborde2 and Y. Renard3

1  Institut de Mathématiques, UMR CNRS 5215, GMM INSA Toulouse, Complexe scientifique de Rangueil, 31077 Toulouse Cedex 4, France
2  Institut de Mathématiques, UMR CNRS 5215, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France
3  Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, F-69621, Villeurbanne, France

Yves.Renard@insa-lyon.fr

Published online: 27 January 2009

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.


Mathematics Subject Classification. 74R99, 74S05, 65N30

Key words: fracture -- finite element method -- Xfem -- reduced basis -- error estimates


© EDP Sciences 2009


What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.