High accuracy analysis of an H-1-Galerkin mixed finite element method for two-dimensional time fractional diffusion equations

doi:10.1016/j.camwa.2017.06.057

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	High accuracy analysis of an H-1-Galerkin mixed finite element method for two-dimensional time fractional diffusion equations
	Shi, Z. G.1,2; Zhao, Y. M.1; Liu, F.3; Tang, Y. F.4,5; Wang, F. L.1; Shi, Y. H.1
	2017-10-15
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	74 期号:8 页码:1903-1914
摘要	In this paper, an H-1-Galerkin mixed finite element approximate scheme is established for a class of two-dimensional time fractional diffusion equations by using the bilinear element, Raviart-Thomas element and L1 time stepping method, which is unconditionally stable and free of LBB condition. And then, without the classical Ritz projection, superclose results for the original variable u in H-1-norm and the flux (p) over right arrow= del u in H(div,Omega)-norm are derived by means of properties of the elements and 1,1 approximation. Furthermore, with the help of the interpolation postprocessing operator, the global superconvergence results for the original variable u in H-1-norm are obtained. Finally, numerical simulations verify that the theoretical results are true on both regular meshes and anisotropic meshes. (C) 2017 Published by Elsevier Ltd.
关键词	Time fractional diffusion equations H-1-Galerkin mixed finite element method Anisotropic mesh L1 approximation Superclose and superconvergence
DOI	10.1016/j.camwa.2017.06.057
语种	英语
资助项目	China Scholarship Council[201308410260] ; National Natural Science Foundation of China[11101381] ; Outstanding Young Talents Training Plan by Xuchang University[[2015]3]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000414889400012
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26804
专题	中国科学院数学与系统科学研究院
通讯作者	Zhao, Y. M.; Liu, F.
作者单位	1.Xuchang Univ, Sch Math & Stat, Xuchang 461000, Peoples R China 2.Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China 3.Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia 4.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Shi, Z. G.,Zhao, Y. M.,Liu, F.,et al. High accuracy analysis of an H-1-Galerkin mixed finite element method for two-dimensional time fractional diffusion equations[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2017,74(8):1903-1914.
APA	Shi, Z. G.,Zhao, Y. M.,Liu, F.,Tang, Y. F.,Wang, F. L.,&Shi, Y. H..(2017).High accuracy analysis of an H-1-Galerkin mixed finite element method for two-dimensional time fractional diffusion equations.COMPUTERS & MATHEMATICS WITH APPLICATIONS,74(8),1903-1914.
MLA	Shi, Z. G.,et al."High accuracy analysis of an H-1-Galerkin mixed finite element method for two-dimensional time fractional diffusion equations".COMPUTERS & MATHEMATICS WITH APPLICATIONS 74.8(2017):1903-1914.