Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation

doi:10.1002/num.22226

	Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation
	Ren, Jincheng 1; Mao, Shipeng2,3 ; Zhang, Jiwei 4
	2018-03-01
发表期刊	NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0749-159X
卷号	34 期号:2 页码:705-730
摘要	In this article, an efficient algorithm for the evaluation of the Caputo fractional derivative and the superconvergence property of fully discrete finite element approximation for the time fractional subdiffusion equation are considered. First, the space semidiscrete finite element approximation scheme for the constant coefficient problem is derived and supercloseness result is proved. The time discretization is based on the L1-type formula, whereas the space discretization is done using, the fully discrete scheme is developed. Under some regularity assumptions, the superconvergence estimate is proposed and analyzed. Then, extension to the case of variable coefficients is also discussed. To reduce the computational cost, the fast evaluation scheme of the Caputo fractional derivative to solve the fractional diffusion equations is designed. Finally, numerical experiments are presented to support the theoretical results.
关键词	fast convolution algorithm finite element method fractional subdiffusion equation fully discrete scheme superconvergence estimate
DOI	10.1002/num.22226
语种	英语
资助项目	National Natural Science Foundation of China[11771035] ; National Natural Science Foundation of China[11601119] ; National Natural Science Foundation of China[11471329] ; National Natural Science Foundation of China[91430216] ; National Natural Science Foundation of China[U1530401] ; National Magnetic Confinement Fusion Science Program of China[2015GB110000] ; Major State Research Development Program of China[2016YFB0201304] ; Youth Innovation Promotion Association of CAS[2016003] ; Science and Technology Program of Henan[162102410003] ; Foundation of Henan Educational Committee[17A110002] ; HASTIT[18HASTIT027]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000423435500014
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29518
专题	计算数学与科学工程计算研究所
通讯作者	Mao, Shipeng
作者单位	1.Henan Univ Econ & Law, Coll Math & Informat Sci, Zhengzhou, Henan, Peoples R China 2.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, LSEC, AMSS, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China 4.Beijing Computat Sci Res Ctr, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Ren, Jincheng,Mao, Shipeng,Zhang, Jiwei. Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2018,34(2):705-730.
APA	Ren, Jincheng,Mao, Shipeng,&Zhang, Jiwei.(2018).Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,34(2),705-730.
MLA	Ren, Jincheng,et al."Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 34.2(2018):705-730.