Patrick Laborde

TL;DR: In this article, the authors study the capabilities of Extended Finite Element Method (XFEM) to achieve accurate computations in non smooth situations such as crack problems, and show that the XFEM method ensures a weaker error than classical finite element methods, but the rate of convergence is not improved when the mesh parameter h is going to zero because of the presence of a singularity.

TL;DR: In this article, the mortar finite element method is applied to contact problems between two elastic bodies, allowing the use of no-matching grids and to glue different discretizations across the contact zone in an optimal way.

TL;DR: In this article, a cutoff function is used to localize the singular enrichment surface, and a quasi-optimal convergence rate is obtained for a variant of the eXtended Finite Element Method.

TL;DR: In this article, a new method dealing with the semi-discretized finite element unilateral contact problem in elastodynamics is presented. But this problem is ill-posed mainly because the nodes on the contact surface have their own inertia.

TL;DR: In this paper, the authors extend the mortar finite element method to handle the unilateral contact model between two deformable bodies and give an upper bound of the convergence rate similar to the one already obtained for compatible meshes.