Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations

被引：148
|
作者：
Bu, Weiping [1 ]
Tang, Yifa [1 ]
Yang, Jiye [1 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2014年 / 276卷
基金：
中国国家自然科学基金;
关键词：
Finite element method; Riesz space fractional diffusion equation; Stability; Convergence; Extrapolation method; ADVECTION-DISPERSION EQUATIONS; NUMERICAL APPROXIMATION; DIFFERENTIAL-EQUATIONS; BOUNDED DOMAINS; SUBDIFFUSION; CONVERGENCE;
D O I：
10.1016/j.jcp.2014.07.023
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this article, a class of two-dimensional Riesz space fractional diffusion equations is considered. Some fractional spaces are established and some equivalences between fractional derivative spaces and fractional Sobolev space are presented. By the Galerkin finite element method and backward difference method, a fully discrete scheme is obtained. According to Lax-Milgram theorem, the existence and uniqueness of the solution to the fully discrete scheme are investigated. The stability and convergence of the scheme are also derived. Finally, some numerical examples are given for verification of our theoretical analysis. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：26 / 38
页数：13
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