A non-conformal eXtended Finite Element approach: Integral matching Xfem

This work is dedicated to the mathematical and numerical analysis of a new Xfem approach: the integral maching Xfem. It is known that the quality of the approximation and the convergence rate of Xfem type methods is broadly influenced by the transition layer between the singular enrichment area and the rest of the domain. In the presented method, this transition layer is replaced by an interface associated with an integral matching condition of mortar type. We prove an optimal convergence result for such a non-conformal approximation method and we perform some numerical experiments showing the advantages of the integral matching Xfem with respect to former Xfem approaches.