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The Scientific World Journal
Volume 2014 (2014), Article ID 982413, 9 pages
http://dx.doi.org/10.1155/2014/982413
Research Article

Leapfrog/Finite Element Method for Fractional Diffusion Equation

1Department of Fundamental Courses, Shanghai Customs College, Shanghai 201204, China
2School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, China

Received 18 January 2014; Accepted 17 February 2014; Published 3 April 2014

Academic Editors: C. Li, A. Sikorskii, and S. B. Yuste

Copyright © 2014 Zhengang Zhao and Yunying Zheng. 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

We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an -error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis.