Abstract and Applied Analysis

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

Jingjun Zhao, Jingyu Xiao, and Yang Xu

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 868035, 15 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450276

Digital Object Identifier
doi:10.1155/2013/868035

Mathematical Reviews number (MathSciNet)
MR3045043

Zentralblatt MATH identifier
1275.65064

Citation

Zhao, Jingjun; Xiao, Jingyu; Xu, Yang. A Finite Element Method for the Multiterm Time-Space Riesz Fractional Advection-Diffusion Equations in Finite Domain. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 868035, 15 pages. doi:10.1155/2013/868035. https://projecteuclid.org/euclid.aaa/1393450276


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