An extended finite element variant for partially unknown crack-tip displacement

Elie Chahine (1) , Patrick Laborde (1) , Yves Renard (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 ICJ - Institut Camille Jordan

In this paper, we introduce a new variant of the extended finite element method (Xfem) allowing an optimal convergence rate when the asymptotic displacement is partially unknown at the crack tip. This variant consists in the addition of an adapted discretization of the asymptotic displacement. We give a mathematical result of quasi-optimal {\it a priori} error estimate which allows to analyze the potentialities of the method. Some computational tests are provided and a comparison is made with the classical Xfem

Domaines: Analyse numérique [math.NA]

Elie Chahine, Patrick Laborde, Yves Renard. An extended finite element variant for partially unknown crack-tip displacement. 2008. ⟨hal-00220469⟩