文献类型：期刊文献

英文题名：Superconvergence of Finite Element Approximations for the Fractional Diffusion-Wave Equation

作者：Ren, Jincheng[1];Long, Xiaonian[2,3,4];Mao, Shipeng[2,3,4];Zhang, Jiwei[5]

通讯作者：Mao, SP[1];Mao, SP[2];Mao, SP[3]

机构：[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

第一机构：河南财经政法大学数学与信息科学学院

通讯机构：[1]corresponding author), Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China;[2]corresponding author), Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100190, Peoples R China;[3]corresponding author), Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China.

年份：2017

卷号：72

期号：3

起止页码：917-935

外文期刊名：JOURNAL OF SCIENTIFIC COMPUTING

收录：;EI(收录号：20170803382459);Scopus(收录号：2-s2.0-85013466637);WOS:【SCI-EXPANDED(收录号:WOS:000408109600001)】；

基金：The research is supported by the Major State Research Development Program of China (No. 2016YFB0201304), National Magnetic Confinement Fusion Science Program of China (No. 2015GB110003), National Natural Science Foundation of China (Nos. 11601119, 11471329, 11526074, 91430216 and U1530401), Youth Innovation Promotion Association of CAS, the Science and Technology Program of Henan (No. 162102410003) and Foundation of Henan Educational Committee (No. 17A110002).

语种：英文

外文关键词：Fractional diffusion-wave equation; Finite element method; Fully discrete scheme; Error estimate

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.