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Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation
Ren, Jincheng1; Mao, Shipeng2,3; Zhang, Jiwei4
2018-03-01
Source PublicationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN0749-159X
Volume34Issue:2Pages:705-730
AbstractIn 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.
Keywordfast convolution algorithm finite element method fractional subdiffusion equation fully discrete scheme superconvergence estimate
DOI10.1002/num.22226
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000423435500014
PublisherWILEY
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29518
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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