Study of Some Optimal XFEM Type Methods

  • Elie Chahine
  • Patrick Laborde
  • Julien Pommier
  • Yves Renard
  • Michel Salaün
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 5)


The XFEM method in fracture mechanics is revisited. A first improvement is considered using an enlarged fixed enrichment subdomain around the crack tip and a bonding condition for the corresponding degrees of freedom. An efficient numerical integration rule is introduced for the nonsmooth enrichment functions. The lack of accuracy due to the transition layer between the enrichment aera and the rest of the domain leads to consider a pointwise matching condition at the boundary of the subdomain. An optimal numerical rate of convergence is then obtained using such a nonconformal method.

Key words

Fracture finite elements XFEM method optimal rate of convergence pointwise matching 


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Copyright information

© Springer 2007

Authors and Affiliations

  • Elie Chahine
    • 1
  • Patrick Laborde
    • 2
  • Julien Pommier
    • 1
  • Yves Renard
    • 1
  • Michel Salaün
    • 3
  1. 1.Laboratoire MIP, CNRS UMR 5640, Complexe scientifique de RangueilINSAToulouseFrance
  2. 2.Laboratoire MIP, CNRS UMR 5640Université P. SabatierToulouse Cedex 4France
  3. 3.ENSICAToulouse Cedex 5France

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