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Volume 9, Issue 4
High Accuracy Analysis of an Anisotropic Nonconforming Finite Element Method for Two-Dimensional Time Fractional Wave Equation

Fenling Wang, Yanmin Zhao, Zhengguang Shi, Yanhua Shi & Yifa Tang

DOI: 10.4208/eajam.260718.060119

East Asian J. Appl. Math., 9 (2019), pp. 797-817.

Published online: 2019-10

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  • Abstract

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 $\mathcal{O}$($h$2 + τ3−$α$) in the broken $H$1-norm is established. For regular and anisotropic meshes, numerical examples are consistent with theoretical results.

  • Keywords

Time fractional wave equation, anisotropic nonconforming quasi-Wilson finite element, Crank-Nicolson scheme, stability, superclose and superconvergence.

  • AMS Subject Headings

65N30, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhaoym@lsec.cc.ac.cn (Yanmin Zhao)

tyf@lsec.cc.ac.cn (Yifa Tang)

  • BibTex
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  • TXT
@Article{EAJAM-9-797, author = {Wang , FenlingZhao , YanminShi , ZhengguangShi , Yanhua and Tang , Yifa}, title = {High Accuracy Analysis of an Anisotropic Nonconforming Finite Element Method for Two-Dimensional Time Fractional Wave Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {4}, pages = {797--817}, abstract = {

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 $\mathcal{O}$($h$2 + τ3−$α$) in the broken $H$1-norm is established. For regular and anisotropic meshes, numerical examples are consistent with theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.260718.060119}, url = {http://global-sci.org/intro/article_detail/eajam/13333.html} }
TY - JOUR T1 - High Accuracy Analysis of an Anisotropic Nonconforming Finite Element Method for Two-Dimensional Time Fractional Wave Equation AU - Wang , Fenling AU - Zhao , Yanmin AU - Shi , Zhengguang AU - Shi , Yanhua AU - Tang , Yifa JO - East Asian Journal on Applied Mathematics VL - 4 SP - 797 EP - 817 PY - 2019 DA - 2019/10 SN - 9 DO - http://doi.org/10.4208/eajam.260718.060119 UR - https://global-sci.org/intro/article_detail/eajam/13333.html KW - Time fractional wave equation, anisotropic nonconforming quasi-Wilson finite element, Crank-Nicolson scheme, stability, superclose and superconvergence. AB -

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 $\mathcal{O}$($h$2 + τ3−$α$) in the broken $H$1-norm is established. For regular and anisotropic meshes, numerical examples are consistent with theoretical results.

Wang , FenlingZhao , YanminShi , ZhengguangShi , Yanhua and Tang , Yifa. (2019). High Accuracy Analysis of an Anisotropic Nonconforming Finite Element Method for Two-Dimensional Time Fractional Wave Equation. East Asian Journal on Applied Mathematics. 9 (4). 797-817. doi:10.4208/eajam.260718.060119
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