357 citations · 864 across the 37 of their papers we have counts for
4 papers · 1 filter
A finite volume scheme for nonlinear degenerate parabolic equations
Marianne Bessemoulin-Chatard, Francis Filbet
We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconduct…
On deterministic approximation of the Boltzmann equation in a bounded domain
Francis Filbet
In this paper we present a fully deterministic method for the numerical solution to the Boltzmann equation of rarefied gas dynamics in a bounded domain for multi-scale problems. Pe…
Numerical study of a nonlinear heat equation for plasma physics
Francis Filbet, Claudia Negulescu, Chang Yang
This paper is devoted to the numerical approximation of a nonlinear temperature balance equation, which describes the heat evolution of a magnetically confined plasma in the edge r…
Analysis of an Asymptotic Preserving Scheme for Relaxation Systems
Francis Filbet, Amélie Rambaud
We study the convergence of a class of asymptotic preserving numerical schemes initially proposed by F. Filbet & S. Jin \cite{filb1} and G. Dimarco & L. Pareschi \cite{DimarcoP} in…