A finite element approximation for grazing collisions

Brigitte Lucquin-Desreux (1) , Simona Mancini (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

In this article, we propose a finite element discretization of the Boltzmann-Lorentz operator for which it is possible to define a grazing collision limit. We illustrate this discretization by considering the evolution of a system of particles in a slab, subject to collisions both with the boundaries and with themselves. A comparison is made with isotropic collisions or with the Laplace-Beltrami operator. Moreover, in the case of multiplying boundary conditions, it is proven by numerical simulations the existence of a critical value the numerical results are compared with previous simulations.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Brigitte Lucquin-Desreux, Simona Mancini. A finite element approximation for grazing collisions. Transport Theory and Statistical Physics, 2003, 32, 3& 4, pp.293-319. ⟨hal-00076838⟩