KMS Of Academy of mathematics and systems sciences, CAS
| Space-time finite element method for the distributed-order time fractional reaction diffusion equations | |
| Bu, Weiping1,2; Ji, Lun3,4; Tang, Yifa3,4; Zhou, Jie1,2 | |
| 2020-06-01 | |
| Source Publication | APPLIED NUMERICAL MATHEMATICS
 |
| ISSN | 0168-9274 |
| Volume | 152Pages:446-465 |
| Abstract | In this paper, we propose a space-time finite element method for the distributed-order time fractional reaction diffusion equations (DOTFRDEs). First, using the composite trapezoidal rule, composite Simpson's rule and Gauss-Legendre quadrature rule to discretize the distributed-order derivative and employing the finite element method both in space and time, three fully discrete finite element schemes for DOTFRDEs are developed. Second, for the obtained numerical schemes, the existence, uniqueness and stability are discussed. Third, under the hypothesis about the singular behavior of exact solution near t = 0, the convergence of these numerical schemes are investigated in detail based on the graded time mesh. Forth, in order to reduce the storage requirement and computational cost of these numerical schemes, an efficient sum-of-exponentials approximation for the kernel t(-a), alpha is an element of (0, 1) is introduced, and the developed space-time finite element schemes are improved. At last, some numerical tests are given to verify the rationality and effectiveness of our method. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved. |
| Keyword | Distributed-order reaction diffusion equation Space-time finite element method Graded time mesh Well-posedness Error estimate Sum-of-exponentials approximation |
| DOI | 10.1016/j.apnum.2019.11.010 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11601460] ; National Natural Science Foundation of China[11771438] ; National Natural Science Foundation of China[11501485] ; Natural Science Foundation of Hunan Province of China[2018113491] ; Natural Science Foundation of Hunan Province of China[2018.0492] ; Project of Scientific Research Fund of Hunan Provincial Science and Technology Department[2018WK4006] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000519653600028 |
| Publisher | ELSEVIER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50935 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Tang, Yifa |
| Affiliation | 1.Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China 2.Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Bu, Weiping,Ji, Lun,Tang, Yifa,et al. Space-time finite element method for the distributed-order time fractional reaction diffusion equations[J]. APPLIED NUMERICAL MATHEMATICS,2020,152:446-465. |
| APA | Bu, Weiping,Ji, Lun,Tang, Yifa,&Zhou, Jie.(2020).Space-time finite element method for the distributed-order time fractional reaction diffusion equations.APPLIED NUMERICAL MATHEMATICS,152,446-465. |
| MLA | Bu, Weiping,et al."Space-time finite element method for the distributed-order time fractional reaction diffusion equations".APPLIED NUMERICAL MATHEMATICS 152(2020):446-465. |
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