A Fully Discrete Discontinuous Galerkin Method for Nonlinear Fractional Fokker‐Planck Equation

Abstract

The fractional Fokker‐Planck equation is often used to characterize anomalous diffusion. In this paper, a fully discrete approximation for the nonlinear spatial fractional Fokker‐Planck equation is given, where the discontinuous Galerkin finite element approach is utilized in time domain and the Galerkin finite element approach is utilized in spatial domain. The priori error estimate is derived in detail. Numerical examples are presented which are inline with the theoretical convergence rate.