Abstract

GUILLEN-OVIEDO, Helen  and  SEQUEIRA, Filánder A.. Analysis of the local discontinuous galerkin method for the Fokker-Planck equation. Rev. Mat [online]. 2016, vol.23, n.2, pp.361-387. ISSN 1409-2433.

In this paper we introduce and analyze the Local Discontinuous Galerkin (LDG) method for the Fokker-Planck equation with homogeneous boundary conditions. In particular, we employ a mixed formulation in which the main unknowns are given by the probability current and the probability density function. We apply known results from functional analysis, to establish that the discrete scheme is well-posed. In addition, error estimates are proved for the fully-discrete method using backward Euler time stepping. Finally, we provide numerical examples exhibiting the good performance of the proposed scheme.

Keywords : Fokker-Planck equation; mixed finite element method; discontinuous Galerkin method; high-order approximations.

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