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

doi:10.1002/num.22226

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation
	Ren, Jincheng 1; Mao, Shipeng2,3 ; Zhang, Jiwei 4
刊名	NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
	2018-03-01
卷号	34 期号:2 页码:705-730
关键词	fast convolution algorithm finite element method fractional subdiffusion equation fully discrete scheme superconvergence estimate
ISSN号	0749-159X
DOI	10.1002/num.22226
英文摘要	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.
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
语种	英语
出版者	WILEY
WOS记录号	WOS:000423435500014
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/29517]
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.