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

doi:10.1016/j.camwa.2016.05.005

	Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations
	Zhao, Yanmin 1,2; Zhang, Yadong 1; Liu, F.2; Turner, I.2; Tang, Yifa3 ; Anh, V.2
	2017-03-15
Source Publication	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
Volume	73 Issue:6 Pages:1087-1099
Abstract	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.
Keyword	Multi-term time-fractional diffusion equation Finite element method L1 approximation Stability Convergence and superconvergence
DOI	10.1016/j.camwa.2016.05.005
Language	英语
Funding Project	China Scholarship Council[201308410260] ; National Natural Science Foundation of China[11101381] ; National Natural Science Foundation of China[11371357] ; National Natural Science Foundation of China[11301040] ; Outstanding Young Talents Training Plan by Xuchang University
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied
WOS ID	WOS:000398875300019
Publisher	PERGAMON-ELSEVIER SCIENCE LTD
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/25128
Collection	计算数学与科学工程计算研究所
Corresponding Author	Liu, F.
Affiliation	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
Recommended Citation GB/T 7714	Zhao, Yanmin,Zhang, Yadong,Liu, F.,et al. Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2017,73(6):1087-1099.
APA	Zhao, Yanmin,Zhang, Yadong,Liu, F.,Turner, I.,Tang, Yifa,&Anh, V..(2017).Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations.COMPUTERS & MATHEMATICS WITH APPLICATIONS,73(6),1087-1099.
MLA	Zhao, Yanmin,et al."Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations".COMPUTERS & MATHEMATICS WITH APPLICATIONS 73.6(2017):1087-1099.

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