Finite element method for a symmetric tempered fractional diffusion equation

被引：22
作者：
Celik, Cem [1 ]
Duman, Melda [1 ]
机构：
[1] Dokuz Eylul Univ, Fac Sci, Dept Math, TR-35160 Izmir, Turkey
来源：
APPLIED NUMERICAL MATHEMATICS | 2017年 / 120卷
关键词：
Tempered fractional derivative; Galerkin finite element method; Crank-Nicolson method; STOCHASTIC-PROCESS; CONVERGENCE; MOTION;
D O I：
10.1016/j.apnum.2017.05.012
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A space fractional diffusion equation involving symmetric tempered fractional derivative of order 1 < alpha < 2 is considered. A Galerkin finite element method is implemented to obtain spatial semi-discrete scheme and first order centered difference in time is used to find a fully discrete scheme for tempered fractional diffusion equation. We construct a variational formulation and show its existence, uniqueness and regularity. Stability and error estimates of numerical scheme are discussed. The theoretical and computational study of accuracy and consistence of the numerical solutions are presented. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：270 / 286
页数：17
相关论文
共 16 条
  • [11] Tempered anomalous diffusion in heterogeneous systems
    Meerschaert, Mark M.
    Zhang, Yong
    Baeumer, Boris
    [J]. GEOPHYSICAL RESEARCH LETTERS, 2008, 35 (17)
  • [12] Tempered fractional calculus
    Sabzikar, Farzad
    Meerschaert, Mark M.
    Chen, Jinghua
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 : 14 - 28
  • [13] Samko A. A., 1993, Fractional Integrals andDerivatives: Theory and Applications
  • [14] Thomee V., 2006, SPRINGER SER COMPUT
  • [15] The numerical simulation of the tempered fractional Black-Scholes equation for European double barrier option
    Zhang, H.
    Liu, F.
    Turner, I.
    Chen, S.
    [J]. APPLIED MATHEMATICAL MODELLING, 2016, 40 (11-12) : 5819 - 5834
  • [16] Modeling mixed retention and early arrivals in multidimensional heterogeneous media using an explicit Lagrangian scheme
    Zhang, Yong
    Meerschaert, Mark M.
    Baeumer, Boris
    LaBolle, Eric M.
    [J]. WATER RESOURCES RESEARCH, 2015, 51 (08) : 6311 - 6337
12