Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation

doi:10.1007/s10915-017-0385-z

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

	Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation
	Ren, Jincheng 1; Long, Xiaonian 2,3,4; Mao, Shipeng2,3,4 ; Zhang, Jiwei 5
刊名	JOURNAL OF SCIENTIFIC COMPUTING
	2017-09-01
卷号	72 期号:3 页码:917-935
关键词	Fractional diffusion-wave equation Finite element method Fully discrete scheme Error estimate
ISSN号	0885-7474
DOI	10.1007/s10915-017-0385-z
英文摘要	In 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.
资助项目	Major 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研究方向	Mathematics
语种	英语
出版者	SPRINGER/PLENUM PUBLISHERS
WOS记录号	WOS:000408109600001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/26508]
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 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
推荐引用方式 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.