Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 171620, 20 pages
http://dx.doi.org/10.1155/2011/171620
Research Article

A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation

Yunying Zheng1 and Zhengang Zhao2,3

1Department of Mathematics, Huaibei Normal University, Huaibei 235000, China
2Department of Fundamental Courses, Shanghai Customs College, Shanghai 201204, China
3Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 13 May 2011; Revised 27 July 2011; Accepted 27 July 2011

Academic Editor: Delfim Soares Jr.

Copyright © 2011 Yunying Zheng and Zhengang Zhao. 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 spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.