A finite element approximation for grazing collisions
Résumé
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.
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