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

Authors

  • Fenling Wang School of Mathematics and Statistics, Xuchang University, Xuchang 461000, China.
  • Yanmin Zhao School of Science, Xuchang University, Xuchang 461000, China
  • Zhengguang Shi School of Economic Mathematics, Southwestern University of Finance and Economic, Chengdu, 611130, China
  • Yanhua Shi School of Mathematics and Statistics, Xuchang University, Xuchang 461000, China.
  • Yifa Tang LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

DOI:

https://doi.org/10.4208/eajam.260718.060119

Keywords:

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

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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Published

2019-10-09

Issue

Vol. 9 No. 4 (2019)

Section

Articles