Abstract and Applied Analysis
Volume 2013 (2013), Article ID 868035, 15 pages
http://dx.doi.org/10.1155/2013/868035
Research Article

A Finite Element Method for the Multiterm Time-Space Riesz Fractional Advection-Diffusion Equations in Finite Domain

Jingjun Zhao, Jingyu Xiao, and Yang Xu

Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China

Received 13 December 2012; Revised 28 February 2013; Accepted 28 February 2013

Academic Editor: Xinan Hao

Copyright © 2013 Jingjun Zhao 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

We present an effective finite element method (FEM) for the multiterm time-space Riesz fractional advection-diffusion equations (MT-TS-RFADEs). We obtain the weak formulation of MT-TS-RFADEs and prove the existence and uniqueness of weak solution by the Lax-Milgram theorem. For multiterm time discretization, we use the Diethelm fractional backward finite difference method based on quadrature. For spatial discretization, we show the details of an FEM for such MT-TS-RFADEs. Then, stability and convergence of such numerical method are proved, and some numerical examples are given to match well with the main conclusions.