357 citations · 864 across the 37 of their papers we have counts for
5 papers · 1 filter
On a discrete framework of hypocoercivity for kinetic equations
Alain Blaustein, Francis Filbet
We propose and study a fully discrete finite volume scheme for the Vlasov-Fokker-Planck equation written as an hyperbolic system using Hermite polynomials in velocity. This approac…
Asymptotically preserving particle methods for strongly magnetizedplasmas in a torus
Francis Filbet, Luis Miguel Miguel Rodrigues
We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subj…
On the convergence of discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system
Marianne Bessemoulin-Chatard, Francis Filbet
We prove the convergence of discontinuous Galerkin approximations for the Vlasov-Poisson system written as an hyperbolic system using Hermite polynomials in velocity. To obtain sta…
Fokker-planck Multi-species Equations In The Adiabatic Asymptotics
Francis Filbet, Claudia Negulescu
The main concern of the present paper is the study of the multi-scale dynamics of thermonuclear fusion plasmas via a multi-species Fokker-Planck kinetic model. One of the goals is…
Concentration phenomena in Fitzhugh-Nagumo's equations: A mesoscopic approach
Alain Blaustein, Francis Filbet
We consider a spatially extended mesoscopic FitzHugh-Nagumo model with strong local interactions and prove that its asymptotic limit converges towards the classical nonlocal reacti…