文献类型：期刊文献

英文题名：Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation

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

通讯作者：Mao, SP[1]

机构：[1]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

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, Inst Computat Math & Sci Engn Comp, LSEC, AMSS, Beijing 100190, Peoples R China.

年份：2018

卷号：34

期号：2

起止页码：705-730

外文期刊名：NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

收录：;EI(收录号：20174604386953);Scopus(收录号：2-s2.0-85033212817);WOS:【SCI-EXPANDED(收录号:WOS:000423435500014)】；

基金：National Natural Science Foundation of China 11771035, 11601119, 11471329, 91430216, U1530401; National Magnetic Confinement Fusion Science Program of China, Grant/Award Numbers: 2015GB110000; The Major State Research Development Program of China, Grant/Award Numbers: 2016YFB0201304; Youth Innovation Promotion Association of CAS, Grant/Award Numbers: 2016003; The Science and Technology Program of Henan, Grant/Award Numbers: 162102410003; Foundation of Henan Educational Committee, Grant/Award Numbers: 17A110002; HASTIT, Grant/Award Numbers: 18HASTIT027

语种：英文

外文关键词：fast convolution algorithm; finite element method; fractional subdiffusion equation; fully discrete scheme; superconvergence estimate

摘要：In 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.