Abstract and Applied Analysis

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

Jingjun Zhao, Jingyu Xiao, and Yang Xu

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 857205, 10 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450279

Digital Object Identifier
doi:10.1155/2013/857205

Mathematical Reviews number (MathSciNet)
MR3035313

Zentralblatt MATH identifier
1275.65055

Citation

Zhao, Jingjun; Xiao, Jingyu; Xu, Yang. Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 857205, 10 pages. doi:10.1155/2013/857205. https://projecteuclid.org/euclid.aaa/1393450279


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