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Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations
Zhao, Yanmin1,2; Zhang, Yadong1; Liu, F.2; Turner, I.2; Tang, Yifa3; Anh, V.2
2017-03-15
Source PublicationCOMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN0898-1221
Volume73Issue:6Pages:1087-1099
AbstractUsing 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.
KeywordMulti-term time-fractional diffusion equation Finite element method L1 approximation Stability Convergence and superconvergence
DOI10.1016/j.camwa.2016.05.005
Language英语
Funding ProjectChina 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 AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000398875300019
PublisherPERGAMON-ELSEVIER SCIENCE LTD
Citation statistics
Cited Times:16[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25128
Collection计算数学与科学工程计算研究所
Affiliation1.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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