Abstract and Applied Analysis
Volume 2013 (2013), Article ID 857205, 10 pages
http://dx.doi.org/10.1155/2013/857205
Research Article

Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations

Jingjun Zhao, Jingyu Xiao, and Yang Xu

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

Received 11 December 2012; Revised 3 February 2013; Accepted 6 February 2013

Academic Editor: Dragoş-Pătru Covei

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

A finite element method (FEM) for multiterm fractional partial differential equations (MT-FPDEs) is studied for obtaining a numerical solution effectively. The weak formulation for MT-FPDEs and the existence and uniqueness of the weak solutions are obtained by the well-known Lax-Milgram theorem. The Diethelm fractional backward difference method (DFBDM), based on quadrature for the time discretization, and FEM for the spatial discretization have been applied to MT-FPDEs. The stability and convergence for numerical methods are discussed. The numerical examples are given to match well with the main conclusions.