High Accuracy Analysis of an Anisotropic Nonconforming Finite Element Method for Two-Dimensional Time Fractional Wave Equation

被引：0
|
作者：
Wang, Fenling [1 ]
Zhao, Yanmin [1 ]
Shi, Zhengguang [2 ]
Shi, Yanhua [1 ]
Tang, Yifa [3 ,4 ]
机构：
[1] Xuchang Univ, Sch Math & Stat, Xuchang 461000, Peoples R China
[2] Southwestern Univ Finance & Econ, Sch Econ Math, Chengdu 611130, Sichuan, Peoples R China
[3] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
[4] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
来源：
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2019年 / 9卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Time fractional wave equation; anisotropic nonconforming quasi-Wilson finite element; Crank-Nicolson scheme; stability; superclose and superconvergence; NUMERICAL-SOLUTION; SUPERCONVERGENCE ANALYSIS; DIFFUSION-EQUATIONS; DIFFERENCE-METHODS; GALERKIN METHOD; APPROXIMATION; SCHEME; STABILITY;
D O I：
10.4208/eajam.260718.060119
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
High-order numerical analysis of a nonconforming finite element method on regular and anisotropic meshes for two dimensional time fractional wave equation is presented. The stability of a fully-discrete approximate scheme based on quasi-Wilson FEM in spatial direction and Crank-Nicolson approximation in temporal direction is proved and spatial global superconvergence and temporal convergence order O(h(2) + tau(3-alpha)) in the broken H-1-norm is established. For regular and anisotropic meshes, numerical examples are consistent with theoretical results.
引用
收藏
页码：797 / 817
页数：21
相关论文
共 50 条
  • [1] Superconvergence analysis of nonconforming finite element method for two-dimensional time-fractional Allen-Cahn equation
    Wei, Yabing
    Zhao, Yanmin
    Wang, Fenling
    Tang, Yifa
    [J]. APPLIED MATHEMATICS LETTERS, 2023, 140
  • [2] Superconvergence analysis of nonconforming finite element method for two-dimensional time fractional diffusion equations
    Zhao, Y.
    Zhang, Y.
    Shi, D.
    Liu, F.
    Turner, I.
    [J]. APPLIED MATHEMATICS LETTERS, 2016, 59 : 38 - 47
  • [3] A NONCONFORMING FINITE-ELEMENT METHOD FOR THE TWO-DIMENSIONAL CAHN-HILLIARD EQUATION
    ELLIOTT, CM
    FRENCH, DA
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1989, 26 (04) : 884 - 903
  • [4] High accuracy analysis of anisotropic finite element method for a class of nonlinear degenerate wave equation
    [J]. Li, Zhiyan, 1600, Journal of Chemical and Pharmaceutical Research, 3/668 Malviya Nagar, Jaipur, Rajasthan, India (06):
  • [5] High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation
    Wang, Lele
    Liao, Xin
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2020, 2020
  • [6] High-accuracy finite element method for 2D time fractional diffusion-wave equation on anisotropic meshes
    Zhang, Y. D.
    Zhao, Y. M.
    Wang, F. L.
    Tang, Y. F.
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (01) : 218 - 230
  • [7] High accuracy analysis of an H1-Galerkin mixed finite element method for two-dimensional time fractional diffusion equations
    Shi, Z. G.
    Zhao, Y. M.
    Liu, F.
    Tang, Y. F.
    Wang, F. L.
    Shi, Y. H.
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (08) : 1903 - 1914
  • [8] 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
  • [9] Alternating Direction Implicit Galerkin Finite Element Method for the Two-Dimensional Time Fractional Evolution Equation
    Li, Limei
    Xu, Da
    [J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2014, 7 (01) : 41 - 57
  • [10] Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation
    Zhao, Yue
    Bu, Weiping
    Zhao, Xuan
    Tang, Yifa
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 350 : 117 - 135
12345