Space-time finite element method for the distributed-order time fractional reaction diffusion equations

doi:10.1016/j.apnum.2019.11.010

	Space-time finite element method for the distributed-order time fractional reaction diffusion equations
	Bu, Weiping 1,3; Ji, Lun 2,4; Tang, Yifa 2,4; Zhou, Jie 1,3
刊名	APPLIED NUMERICAL MATHEMATICS
	2020-06-01
卷号	152 页码:446-465
关键词	Distributed-order reaction diffusion equation Space-time finite element method Graded time mesh Well-posedness Error estimate Sum-of-exponentials approximation
ISSN号	0168-9274
DOI	10.1016/j.apnum.2019.11.010
英文摘要	In this paper, we propose a space-time finite element method for the distributed-order time fractional reaction diffusion equations (DOTFRDEs). First, using the composite trapezoidal rule, composite Simpson's rule and Gauss-Legendre quadrature rule to discretize the distributed-order derivative and employing the finite element method both in space and time, three fully discrete finite element schemes for DOTFRDEs are developed. Second, for the obtained numerical schemes, the existence, uniqueness and stability are discussed. Third, under the hypothesis about the singular behavior of exact solution near t = 0, the convergence of these numerical schemes are investigated in detail based on the graded time mesh. Forth, in order to reduce the storage requirement and computational cost of these numerical schemes, an efficient sum-of-exponentials approximation for the kernel t(-a), alpha is an element of (0, 1) is introduced, and the developed space-time finite element schemes are improved. At last, some numerical tests are given to verify the rationality and effectiveness of our method. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
资助项目	National Natural Science Foundation of China[11601460] ; National Natural Science Foundation of China[11771438] ; National Natural Science Foundation of China[11501485] ; Natural Science Foundation of Hunan Province of China[2018113491] ; Natural Science Foundation of Hunan Province of China[2018.0492] ; Project of Scientific Research Fund of Hunan Provincial Science and Technology Department[2018WK4006]
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000519653600028
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50934]
专题	中国科学院数学与系统科学研究院
通讯作者	Tang, Yifa
作者单位	1.Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Bu, Weiping,Ji, Lun,Tang, Yifa,et al. Space-time finite element method for the distributed-order time fractional reaction diffusion equations[J]. APPLIED NUMERICAL MATHEMATICS,2020,152:446-465.
APA	Bu, Weiping,Ji, Lun,Tang, Yifa,&Zhou, Jie.(2020).Space-time finite element method for the distributed-order time fractional reaction diffusion equations.APPLIED NUMERICAL MATHEMATICS,152,446-465.
MLA	Bu, Weiping,et al."Space-time finite element method for the distributed-order time fractional reaction diffusion equations".APPLIED NUMERICAL MATHEMATICS 152(2020):446-465.