Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation

doi:10.1016/j.jcp.2017.08.051

	Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation
	Zhao, Yue 1; Bu, Weiping 2; Zhao, Xuan 3; Tang, Yifa1,4
	2017-12-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	350 页码:117-135
摘要	In this paper, we consider the Galerkin finite element method for the two-dimensional space and time fractional Bloch-Torrey equation (2D-STFBTE). Utilizing the L2-1 sigma formula to discretize temporal Caputo derivative, we obtain the local truncation error with O (iota H3-Q) in the temporal direction, where a is the order of time fractional derivative. Furthermore, the semi-discrete form for the problem is given and, the stability and convergence of the semi-discrete variational formulation are rigorously proved in L-2 norm and fractional norm respectively. Then, we derive a fully discrete scheme for the 2D-STFBTE and investigate its convergence theoretically. Finally, extensive numerical results based on linear piecewise polynomials verify the theoretical results and show the effectiveness of the proposed scheme. (C) 2017 Elsevier Inc. All rights reserved.
关键词	Space and time fractional Bloch-Torrey equation Galerkin finite element method L2-1(sigma) formula Stability Convergence
DOI	10.1016/j.jcp.2017.08.051
语种	英语
资助项目	State Key Program of National Natural Science Foundation of China[11631013] ; National Natural Science Foundation of China[11371357] ; National Natural Science Foundation of China[11601460] ; Research Foundation of Education Commission of Hunan Province of China[1601540] ; ITER-China Program[2014GB124005]
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000413379000007
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26785
专题	计算数学与科学工程计算研究所
通讯作者	Zhao, Yue
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China 3.Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Zhao, Yue,Bu, Weiping,Zhao, Xuan,et al. Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2017,350:117-135.
APA	Zhao, Yue,Bu, Weiping,Zhao, Xuan,&Tang, Yifa.(2017).Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation.JOURNAL OF COMPUTATIONAL PHYSICS,350,117-135.
MLA	Zhao, Yue,et al."Galerkin finite element method for two-dimensional space and time fractional Bloch-Torrey equation".JOURNAL OF COMPUTATIONAL PHYSICS 350(2017):117-135.