Finite difference/spectral element method for one and two-dimensional Riesz space fractional advection-dispersion equations

被引：6
|
作者：
Saffarian, Marziyeh [1 ]
Mohebbi, Akbar [1 ]
机构：
[1] Univ Kashan, Fac Math Sci, Dept Appl Math, Kashan, Iran
来源：
MATHEMATICS AND COMPUTERS IN SIMULATION | 2022年 / 193卷
关键词：
Spectral element method; Stability; Error estimate; Advection dispersion equation; Riesz space fractional derivative; SPECTRAL GALERKIN METHODS; IMPLICIT RUNGE-KUTTA; NUMERICAL-SOLUTION; DIFFUSION; APPROXIMATION; TIME; CONVERGENCE; STABILITY; DYNAMICS; FLOW;
D O I：
10.1016/j.matcom.2021.10.020
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper, we propose an efficient numerical method for the solution of one and two dimensional Riesz space fractional advection-dispersion equation. To this end, we use the Crank-Nicolson scheme to discretize this equation in temporal direction and prove that the semi-discrete scheme is unconditionally stable. Then, we apply the spectral element method in spatial directions and obtain the fully discrete scheme. We present an error estimate for the fully discrete scheme. The presented numerical results demonstrate the accuracy and efficiency of the proposed method in comparison with other schemes in literature. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：348 / 370
页数：23
相关论文
共 50 条
  • [1] Finite element method for two-dimensional space-fractional advection-dispersion equations
    Zhao, Yanmin
    Bu, Weiping
    Huang, Jianfei
    Liu, Da-Yan
    Tang, Yifa
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 257 : 553 - 565
  • [2] Stability and convergence of difference methods for two-dimensional Riesz space fractional advection-dispersion equations with delay
    Heris, Mahdi Saedshoar
    Javidi, Mohammad
    Ahmad, Bashir
    [J]. COMPUTATIONAL AND MATHEMATICAL METHODS, 2020, 2 (03)
  • [3] A Comparative Study of Finite Element and Finite Difference Methods for Two-Dimensional Space-Fractional Advection-Dispersion Equation
    Pang, Guofei
    Chen, Wen
    Sze, Kam Yim
    [J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2016, 8 (01) : 166 - 186
  • [4] HIGH-ORDER NUMERICAL METHOD FOR TWO-DIMENSIONAL RIESZ SPACE FRACTIONAL ADVECTION-DISPERSION EQUATION
    Borhanifar, Abdollah
    Ragusa, Maria Alessandra
    Valizadeh, Sohrab
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2021, 26 (10): : 5495 - 5508
  • [5] Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations
    Bu, Weiping
    Tang, Yifa
    Yang, Jiye
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 276 : 26 - 38
  • [6] Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations
    [J]. Tang, Y. (tyf@lsec.cc.ac.cn), 1600, Academic Press Inc. (276):
  • [7] Finite difference approximations for fractional advection-dispersion flow equations
    Meerschaert, MM
    Tadjeran, C
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 172 (01) : 65 - 77
  • [8] Analytical and Numerical Solutions of Riesz Space Fractional Advection-Dispersion Equations with Delay
    Heris, Mahdi Saedshoar
    Javidi, Mohammad
    Ahmad, Bashir
    [J]. CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2019, 121 (01): : 249 - 272
  • [9] A stable explicitly solvable numerical method for the Riesz fractional advection-dispersion equations
    Zhang, Jingyuan
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2018, 332 : 209 - 227
  • [10] Space-fractional advection-dispersion equations by the Kansa method
    Pang, Guofei
    Chen, Wen
    Fu, Zhuojia
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 : 280 - 296
12345