VAUCHELET , Nicolas

A numerical analysis of upwind type schemes for the nonlinear nonlocal aggregation equation is provided. In this approach, the aggregation equation is interpreted as a conservative transport equation driven by a nonlocal nonlinear velocity field with low regularity. In particular, we allow the interacting potential to be pointy, in which case...

An analysis of the error of the upwind scheme for transport equation with discontinuous coefficients is provided. We consider here a velocity field that is bounded and one-sided Lipschitz continuous. In this framework, solutions are defined in the sense of measures along the lines of Poupaud and Rascle's work. We study the convergence order of...

In this work, we consider the computation of the boundary conditions for the linearized Euler-Poisson derived from the BGK kinetic model in the small mean free path regime. Boundary layers are generated from the fact that the incoming kinetic flux might be far from the thermodynamical equilibrium. In [2], the authors propose a method to compute...

In this work, we consider the computation of the boundary conditions for the linearized Euler-Poisson derived from the BGK kinetic model in the small mean free path regime. Boundary layers are generated from the fact that the incoming kinetic flux might be far from the thermodynamical equilibrium. In [2], the authors propose a method to compute...

The aggregation equation is a nonlocal and nonlinear conservation law commonly used to describe the collective motion of individuals interacting together. When interacting potentials are pointy, it is now well established that solutions may blow up in finite time but global in time weak measure valued solutions exist. In this paper we focus on...