Optimal convergence analysis for the extended finite element method

Serge Nicaise (1) , Yves Renard (2) , Elie Chahine (3)

1 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
3 Laboratory for Nuclear Materials

We establish some optimal a priori error estimate on some variants of the eXtended Finite Element Method (Xfem), namely the Xfem with a cut-off function and the standard Xfem with a fixed enrichment area. The results are established for the Lame system (homogeneous isotropic elasticity) and the Laplace problem. The convergence of the numerical stress intensity factors is also investigated. We show some numerical experiments which corroborate the theoretical results.

Mots clés: error estimates; stress intensity factors; extended finite element method

Domaines: Analyse numérique [math.NA]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Serge Nicaise, Yves Renard, Elie Chahine. Optimal convergence analysis for the extended finite element method. International Journal for Numerical Methods in Engineering, 2011, 86, pp.528-548. ⟨10.1002/nme.3092⟩. ⟨hal-00339853v2⟩