High Accuracy Analysis of an Anisotropic Nonconforming Finite Element Method for Two-Dimensional Time Fractional Wave Equation
Year: 2019
Author: Fenling Wang, Yanmin Zhao, Zhengguang Shi, Yanhua Shi, Yifa Tang
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.260718.060119
East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 4 : pp. 797–817
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Time fractional wave equation anisotropic nonconforming quasi-Wilson finite element Crank-Nicolson scheme stability superclose and superconvergence.