KMS Of Academy of mathematics and systems sciences, CAS
| Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations | |
Wei, Ya-bing1,2; Zhao, Yan-min1; Shi, Zheng-guang3; Wang, Fen-ling1; Tang, Yi-fa4,5
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| 2018-10-01 | |
| Source Publication | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
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| ISSN | 0168-9673 |
| Volume | 34Issue:4Pages:828-841 |
| Abstract | In this paper, high-order numerical analysis of finite element method (FEM) is presented for two-dimensional multi-term time-fractional diffusion-wave equation (TFDWE). First of all, a fully-discrete approximate scheme for multi-term TFDWE is established, which is based on bilinear FEM in spatial direction and Crank-Nicolson approximation in temporal direction, respectively. Then the proposed scheme is proved to be unconditionally stable and convergent. And then, rigorous proofs are given here for superclose properties in H-1-norm and temporal convergence in L-2-norm with order O(h(2) + tau(3-alpha)) where h and tau are the spatial size and time step, respectively. At the same time, theoretical analysis of global superconvergence in H-1-norm is derived by interpolation postprocessing technique. At last, numerical example is provided to demonstrate the theoretical analysis. |
| Keyword | multi-term time-fractional diffusion-wave equation bilinear finite element method Crank-Nicolson approximation stability convergence and superconvergence |
| DOI | 10.1007/s10255-018-0795-1 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11771438] ; National Natural Science Foundation of China[11471296] ; Key Scientific Research Projects in Universities of Henan Province[19B110013] ; Program for Scientific and Technological Innovation Talents in Universities of Henan Province[19HASTIT025] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000446425100017 |
| Publisher | SPRINGER HEIDELBERG |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/31481 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Zhao, Yan-min |
| Affiliation | 1.Xuchang Univ, Sch Math & Stat, Xuchang 461000, Peoples R China 2.Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China 3.Southwestern Univ Finance & Econ, Sch Econ Math, Chengdu 611130, Sichuan, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Wei, Ya-bing,Zhao, Yan-min,Shi, Zheng-guang,et al. Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2018,34(4):828-841. |
| APA | Wei, Ya-bing,Zhao, Yan-min,Shi, Zheng-guang,Wang, Fen-ling,&Tang, Yi-fa.(2018).Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,34(4),828-841. |
| MLA | Wei, Ya-bing,et al."Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 34.4(2018):828-841. |
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