Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations

被引：48

作者：

Zhao, Yanmin ^{[1
,2
]}

Zhang, Yadong ^{[1
]}

Liu, F. ^{[2
]}

Turner, I. ^{[2
]}

Tang, Yifa ^{[3
]}

Anh, V. ^{[2
]}

机构：

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

[2] Queensland Univ Technol, Sch Math Sci, GPO Box 2434, Brisbane, Qld 4001, Australia

[3] Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 73卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Multi-term time-fractional diffusion equation; Finite element method; L1; approximation; Stability Convergence and superconvergence; FINITE-ELEMENT-METHOD; DIFFERENCE SCHEME; ORDER; APPROXIMATION;

D O I：

10.1016/j.camwa.2016.05.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using finite element method in spatial direction and classical L1 approximation in temporal direction, a fully-discrete scheme is established for a class of two-dimensional multi-term time fractional diffusion equations with Caputo fractional derivatives. The stability analysis of the approximate scheme is proposed. The spatial global superconvergence and temporal convergence of order O(h(2) + tau(2-alpha)) for the original variable in H-1-norm is presented by means of properties of bilinear element and interpolation postprocessing technique, where h and tau are the step sizes in space and time, respectively. Finally, several numerical examples are implemented to evaluate the efficiency of the theoretical results. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：1087 / 1099

页数：13

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