Superconvergence analysis of nonconforming finite element method for two-dimensional time fractional diffusion equations

被引：41

作者：

Zhao, Y. ^{[1
,2
]}

Zhang, Y. ^{[1
]}

Shi, D. ^{[3
]}

Liu, F. ^{[2
]}

Turner, I. ^{[2
]}

机构：

[1] Xuchang Univ, Sch Math & Stat, Xuchang 461000, Peoples R China

[2] Queensland Univ Technol, Brisbane, Qld 4001, Australia

[3] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2016年 / 59卷

基金：

中国国家自然科学基金;

关键词：

Time-fractional diffusion equations; Quasi-Wilson element; L1; approximation; Fully-discrete scheme; Superclose and superconvergence; SUBDIFFUSION EQUATION; NUMERICAL ALGORITHMS; DIFFERENCE SCHEME; GALERKIN METHOD; SPECTRAL METHOD; APPROXIMATION; CONVERGENCE;

D O I：

10.1016/j.aml.2016.03.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By means of spatial quasi-Wilson nonconforming finite element and classical L1 approximation, an unconditionally stable fully-discrete scheme for two-dimensional time fractional diffusion equations is established. Moreover, convergence results in L-2-norm and broken H-1-norm and the corresponding superclose and superconvergence results in spatial direction in broken H-1-norm are obtained by use of special properties of quasi-Wilson element. At the same time, the optimal order error estimate in temporal direction is derived by dealing with fractional derivative skillfully. Finally, numerical results demonstrate that the approximate scheme provides valid and efficient way for solving the time-fractional diffusion equation. Crown Copyright (C) 2016 Published by Elsevier Ltd. All rights reserved.

引用

页码：38 / 47

页数：10

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