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

doi:10.1007/s10915-017-0385-z

	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
	2017-09-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	72 期号:3 页码:917-935
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.
关键词	Fractional diffusion-wave equation Finite element method Fully discrete scheme Error estimate
DOI	10.1007/s10915-017-0385-z
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000408109600001
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26509
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.