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 - <p style="text-align: justify;">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 $\mathcal{O}$($h$<sup>2</sup> + τ<sup>3−$α$</sup>) in
the broken $H$<sup>1</sup>-norm is established. For regular and anisotropic meshes, numerical examples are consistent with theoretical results.</p>