Approximation par la méthode des éléments finis de la formulation en domaine régulier de problèmes de fissures

The discretization by various mixed finite element methods of a new variational formulation of crack problems is considered. The new formulation, called the smooth domain method, is derived for crack problems in the case of a simplified model of an elastic membrane. Inequality type boundary conditions are prescribed at the crack faces. The resulting model takes the form of an unilateral contact problem on the crack. The mathematical analysis for the method leads to optimal convergence rates, as given in this Note. To cite this article: Z. Belhachmi et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).