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
相关论文
共 50 条
  • [21] Finite Difference/Element Method for a Two-Dimensional Modified Fractional Diffusion Equation
    Zhang, Na
    Deng, Weihua
    Wu, Yujiang
    [J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2012, 4 (04) : 496 - 518
  • [22] Galerkin finite element method for time-fractional stochastic diffusion equations
    Guang-an Zou
    [J]. Computational and Applied Mathematics, 2018, 37 : 4877 - 4898
  • [23] Galerkin finite element method for time-fractional stochastic diffusion equations
    Zou, Guang-an
    [J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (04): : 4877 - 4898
  • [24] Superconvergence analysis of an H1-Galerkin mixed finite element method for two-dimensional multi-term time fractional diffusion equations
    Shi, Zhengguang
    Zhao, Yanmin
    Tang, Yifa
    Wang, Fenling
    Shi, Yanhua
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (09) : 1845 - 1857
  • [25] ADI Finite Element Galerkin Methods for Two-dimensional Tempered Fractional Integro-differential Equations
    Qiu, Wenlin
    Fairweather, Graeme
    Yang, Xuehua
    Zhang, Haixiang
    [J]. CALCOLO, 2023, 60 (03)
  • [26] ADI Finite Element Galerkin Methods for Two-dimensional Tempered Fractional Integro-differential Equations
    Wenlin Qiu
    Graeme Fairweather
    Xuehua Yang
    Haixiang Zhang
    [J]. Calcolo, 2023, 60
  • [27] Galerkin finite element methods for two-dimensional RLW and SRLW equations
    Gao, Yali
    Mei, Liquan
    [J]. APPLICABLE ANALYSIS, 2018, 97 (13) : 2288 - 2312
  • [28] Crank-Nicolson ADI Galerkin Finite Element Methods for Two Classes of Riesz Space Fractional Partial Differential Equations
    Chen, An
    [J]. CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2020, 123 (03): : 917 - 939
  • [29] Implicit Runge-Kutta and spectral Galerkin methods for the two-dimensional nonlinear Riesz space fractional diffusion equation
    Zhao, Jingjun
    Zhang, Yanming
    Xu, Yang
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2020, 386
  • [30] SOLVING FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS BY PETROV-GALERKIN FINITE ELEMENT METHOD
    Esen, A.
    Ucar, Y.
    Yagmurlu, M.
    Tasbozan, O.
    [J]. TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2014, 4 (02): : 155 - 168
12345