Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation
文献类型：期刊论文
| 作者 | Ren, Jincheng1; Mao, Shipeng2,3 ; Zhang, Jiwei4
|
| 刊名 | NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2018-03-01 |
| 卷号 | 34期号:2页码:705-730 |
| 关键词 | fast convolution algorithm finite element method fractional subdiffusion equation fully discrete scheme superconvergence estimate |
| ISSN号 | 0749-159X |
| DOI | 10.1002/num.22226 |
| 英文摘要 | 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. |
| 资助项目 | National Natural Science Foundation of China[11771035] ; National Natural Science Foundation of China[11601119] ; National Natural Science Foundation of China[11471329] ; National Natural Science Foundation of China[91430216] ; National Natural Science Foundation of China[U1530401] ; National Magnetic Confinement Fusion Science Program of China[2015GB110000] ; Major State Research Development Program of China[2016YFB0201304] ; Youth Innovation Promotion Association of CAS[2016003] ; Science and Technology Program of Henan[162102410003] ; Foundation of Henan Educational Committee[17A110002] ; HASTIT[18HASTIT027] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000423435500014 |
| 出版者 | WILEY |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/29517]  |
| 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, 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 |
| 推荐引用方式 GB/T 7714 | Ren, Jincheng,Mao, Shipeng,Zhang, Jiwei. Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2018,34(2):705-730. |
| APA | Ren, Jincheng,Mao, Shipeng,&Zhang, Jiwei.(2018).Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,34(2),705-730. |
| MLA | Ren, Jincheng,et al."Fast evaluation and high accuracy finite element approximation for the time fractional subdiffusion equation".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 34.2(2018):705-730. |
入库方式： OAI收割
来源：数学与系统科学研究院
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