We present a non-diffusive and contact discontinuity capturing scheme for linear advection and compressible Euler system. In the case of advection, this scheme is equivalent to the Ultra-Bee limiter… (More)

In this paper, we derive non-dissipative stable and entropy satisfying finite volume schemes for scalar PDEs. It is based on the previous analysis of [20], which deals with general reconstruction… (More)

We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keep… (More)

We provide a probabilistic analysis of the upwind scheme for d-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula… (More)

The Lifschitz–Slyozov system describes the dynamics of mass exchanges between macro–particles and monomers in the theory of coarsening. We consider a variant of the classical model where monomers are… (More)

We are interested in a problem arising for instance in elastoplasticity modeling, which consists in a system of partial differential equations and a constraint specifying that the solution should… (More)

We study a family of non linear schemes for the numerical solution of linear advection on arbitrary grids in several space dimension. A proof of weak convergence of the family of schemes is given,… (More)

This work is devoted to the coupling of two fluid models, such as two Euler systems in Lagrangian coordinates, at a fixed interface. We define coupling conditions which can be expressed in terms of… (More)

We present in this paper several results concerning a simple model of interaction between an inviscid fluid, modeled by the Burgers equation, and a particle, assumed to be point-wise. It is composed… (More)