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Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation
Ren, Jincheng1; Long, Xiaonian2,3,4; Mao, Shipeng2,3,4; Zhang, Jiwei5
2017-09-01
Source PublicationJOURNAL OF SCIENTIFIC COMPUTING
ISSN0885-7474
Volume72Issue:3Pages:917-935
AbstractIn this paper, the error estimates of fully discrete finite element approximation for the time fractional diffusion-wave equation are discussed. Based on the standard Galerkin finite element method approach for the spatial discretization and the L1 formula for the approximation of the time fractional derivative, the fully discrete scheme for solving the constant coefficient fractional diffusion-wave equation is obtained and the superconvergence estimate is proposed and analyzed. Further, a fully discrete finite element scheme is presented for solving the variable coefficient fractional diffusion-wave equation and the corresponding error estimates are also established. Finally, numerical experiments are included to support the theoretical results.
KeywordFractional diffusion-wave equation Finite element method Fully discrete scheme Error estimate
DOI10.1007/s10915-017-0385-z
Language英语
Funding ProjectMajor State Research Development Program of China[2016YFB0201304] ; National Magnetic Confinement Fusion Science Program of China[2015GB110003] ; National Natural Science Foundation of China[11601119] ; National Natural Science Foundation of China[11471329] ; National Natural Science Foundation of China[11526074] ; National Natural Science Foundation of China[91430216] ; National Natural Science Foundation of China[U1530401] ; Youth Innovation Promotion Association of CAS ; Science and Technology Program of Henan[162102410003] ; Foundation of Henan Educational Committee[17A110002]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000408109600001
PublisherSPRINGER/PLENUM PUBLISHERS
Citation statistics
Cited Times:7[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26509
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 450045, Henan, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
5.Beijing Computat Sci Res Ctr, Beijing 100094, Peoples R China
Recommended Citation
GB/T 7714
Ren, Jincheng,Long, Xiaonian,Mao, Shipeng,et al. Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation[J]. JOURNAL OF SCIENTIFIC COMPUTING,2017,72(3):917-935.
APA Ren, Jincheng,Long, Xiaonian,Mao, Shipeng,&Zhang, Jiwei.(2017).Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation.JOURNAL OF SCIENTIFIC COMPUTING,72(3),917-935.
MLA Ren, Jincheng,et al."Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation".JOURNAL OF SCIENTIFIC COMPUTING 72.3(2017):917-935.
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