Mixed finite-element method for multi-term time-fractional diffusion and diffusion-wave equations

被引：27
|
作者：
Li, Meng [1 ,3 ]
Huang, Chengming [1 ,2 ]
Ming, Wanyuan [1 ]
机构：
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China
[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Hubei, Peoples R China
[3] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China
来源：
COMPUTATIONAL & APPLIED MATHEMATICS | 2018年 / 37卷 / 02期
关键词：
Time-fractional diffusion equations; Time-fractional diffusion-wave equations; Mixed finite-element method; Stability analysis; Error estimates; DISCONTINUOUS GALERKIN METHOD; NUMERICAL-METHODS; SPACE; APPROXIMATIONS;
D O I：
10.1007/s40314-017-0447-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, numerical theory based on the mixed finite-element method and finite difference analog of the Caputo fractional derivative for multi-term time-fractional diffusion equations and diffusion-wave equations is analyzed. The unconditional stability and convergence results are proved for the two resulting fully discrete schemes. Finally, the obtained results are supported by numerical experiments carried out for some test problems.
引用
收藏
页码：2309 / 2334
页数：26
相关论文
共 50 条
  • [21] High-order compact finite difference method for the multi-term time fractional mixed diffusion and diffusion-wave equation
    Yu, Bo
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (08) : 6526 - 6539
  • [22] Finite Element Scheme with H2N2 Interpolation for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation
    Zhang, Huiqin
    Chen, Yanping
    Zhou, Jianwei
    Wang, Yang
    ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2024,
  • [23] An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations
    Liu, Zeting
    Liu, Fawang
    Zeng, Fanhai
    APPLIED NUMERICAL MATHEMATICS, 2019, 136 : 139 - 151
  • [24] Finite element multigrid method for multi-term time fractional advection diffusion equations
    Bu, Weiping
    Liu, Xiangtao
    Tang, Yifa
    Yang, Jiye
    INTERNATIONAL JOURNAL OF MODELING SIMULATION AND SCIENTIFIC COMPUTING, 2015, 6 (01)
  • [25] A numerical treatment of the two-dimensional multi-term time-fractional mixed sub-diffusion and diffusion-wave equation
    Ezz-Eldien, S. S.
    Doha, E. H.
    Wang, Y.
    Cai, W.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 91
  • [26] A unified numerical scheme for the multi-term time fractional diffusion and diffusion-wave equations with variable coefficients
    Chen, Hu
    Lu, Shujuan
    Chen, Wenping
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 330 : 380 - 397
  • [27] An algorithm for solving multi-term diffusion-wave equations of fractional order
    Jafari, M. A.
    Aminataei, A.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (03) : 1091 - 1097
  • [28] A Galerkin Finite Element Method to Solve Fractional Diffusion and Fractional Diffusion-Wave Equations
    Esen, Alaattin
    Ucar, Yusuf
    Yagmurlu, Nuri
    Tasbozan, Orkun
    MATHEMATICAL MODELLING AND ANALYSIS, 2013, 18 (02) : 260 - 273
  • [29] Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations
    Ya-bing WEI
    Yan-min ZHAO
    Zheng-guang SHI
    Fen-ling WANG
    Yi-fa TANG
    Acta Mathematicae Applicatae Sinica, 2018, 34 (04) : 828 - 841
  • [30] Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative
    Cao, Fangfang
    Zhao, Yanmin
    Wang, Fenling
    Shi, Yanhua
    Yao, Changhui
    ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2022,
12345