Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 279038, 26 pages
doi:10.1155/2010/279038
Research Article

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

Yunying Zheng,1,2 Changpin Li,1 and Zhengang Zhao1

1Department of Mathematics, Shanghai University, Shanghai 200444, China
2Department of Mathematics, Huainan Normal University, Huainan 232038, China

Received 13 July 2010; Revised 16 September 2010; Accepted 19 October 2010

Academic Editor: J. Jiang

Copyright © 2010 Yunying Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.