Computer simulation of fracture processes remains a challenge for many industrial modelling problems. In a classical finite element method, the non-smooth displacement near the crack tip is capturedâ€¦ (More)

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 enrichmentâ€¦ (More)

The purpose of this paper is to present a new fictitious domain approach inspired by the extended finite element method introduced by MoÃ«s, Dolbow and Belytschko in [18]. An optimal method isâ€¦ (More)

We study three mixed linear finite element methods for the numerical simulation of the two-dimensional Signorini problem. Applying Falkâ€™s Lemma and saddle point theory to the resulting discrete mixedâ€¦ (More)

Abstract. The purpose of this paper is to study the solutions to the Signorini problem with Coulomb friction (the so-called Coulomb problem). Some optimal a priori estimates are given and aâ€¦ (More)

The present paper is concerned with the unilateral contact model and the Coulomb friction law in linear elastostatics. We consider a mixed formulation in which the unknowns are the displacement fieldâ€¦ (More)

Several fixed point strategies and Uzawa algorithms (for classical and augmented Lagrangian formulations) are presented to solve the unilateral contact problem with Coulomb friction. These methodsâ€¦ (More)

The purpose of this paper is to present a new family of numerical methods for the approximation of second order hyperbolic partial differential equations submitted to a convex constraint on theâ€¦ (More)

The aim of this Note is to give a convergence result for a variant of the eXtended Finite Element Method (XFEM) on cracked domains using a cut-off function to localize the singular enrichment area.â€¦ (More)