A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient

doi:10.1016/j.camwa.2018.11.029

	A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient
	Wang, Fenling 1; Zhao, Yanmin 1; Chen, Chen 2; Wei, Yabing 3; Tang, Yifa2,4
	2019-09-01
Source Publication	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
Volume	78 Issue:5 Pages:1288-1301
Abstract	Based on the spatial quasi-Wilson nonconforming finite element method and temporal L2 - 1(sigma) , formula, a fully-discrete approximate scheme is proposed for a two-dimensional time-fractional diffusion equations with variable coefficient on anisotropic meshes. In order to demonstrate the stable analysis and error estimates, several lemmas are provided, which focus on high accuracy about projection and superclose estimate between the interpolation and projection. Unconditionally stable analysis are derived in L-2-norm and broken H-1-norm. Moreover, convergence result of accuracy O(h(2) + tau(2)) and superclose property of accuracy O(h(2) + tau(2)) are deduced by combining interpolation with projection, where h and tau are the step sizes in space and time, respectively. And then, the global superconvergence is presented by employing interpolation post processing operator. Finally, numerical results are provided to demonstrate the validity of the theoretical analysis. (C) 2018 Elsevier Ltd. All rights reserved.
Keyword	Time-fractional diffusion equations Variable coefficient Quasi-Wilson nonconforming anisotropic finite element L2-1(sigma) formula Stability Superclose and superconvergence
DOI	10.1016/j.camwa.2018.11.029
Language	英语
Funding Project	National Natural Science Foundation of China[11771438] ; National Natural Science Foundation of China[11471296] ; Key Scientific Research Projects in Universities of Henan Province, China[198110013] ; Program for Scientific and Technological Innovation Talents in Universities of Henan Province, China[19HASTIT025]
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied
WOS ID	WOS:000482248100005
Publisher	PERGAMON-ELSEVIER SCIENCE LTD
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/35478
Collection	计算数学与科学工程计算研究所
Corresponding Author	Zhao, Yanmin; Tang, Yifa
Affiliation	1.Xuchang Univ, Sch Math & Stat, Xuchang 461000, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
Recommended Citation GB/T 7714	Wang, Fenling,Zhao, Yanmin,Chen, Chen,et al. A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2019,78(5):1288-1301.
APA	Wang, Fenling,Zhao, Yanmin,Chen, Chen,Wei, Yabing,&Tang, Yifa.(2019).A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient.COMPUTERS & MATHEMATICS WITH APPLICATIONS,78(5),1288-1301.
MLA	Wang, Fenling,et al."A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient".COMPUTERS & MATHEMATICS WITH APPLICATIONS 78.5(2019):1288-1301.

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