Keywords
mixed finite element method
discontinuous Galerkin method
high-order approximations
ecuación de Fokker-Planck
método de elemento finito mixto
método de Galerkin discontinuo
aproximaciones de alto orden
How to Cite
Abstract
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.
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