Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations
文献类型：期刊论文
| 作者 | Zhao, Yanmin1; Chen, Pan2; Bu, Weiping3; Liu, Xiangtao4; Tang, Yifa5
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| 刊名 | JOURNAL OF SCIENTIFIC COMPUTING
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| 出版日期 | 2017 |
| 卷号 | 70期号:1页码:407-428 |
| 关键词 | Mixed finite element methods L1 method Time-fractional diffusion equation Unconditional stability Superconvergence and convergence |
| ISSN号 | 0885-7474 |
| DOI | 10.1007/s10915-015-0152-y |
| 英文摘要 | Based on spatial conforming and nonconforming mixed finite element methods combined with classical L1 time stepping method, two fully-discrete approximate schemes with unconditional stability are first established for the time-fractional diffusion equation with Caputo derivative of order . As to the conforming scheme, the spatial global superconvergence and temporal convergence order of for both the original variable u in -norm and the flux in -norm are derived by virtue of properties of bilinear element and interpolation postprocessing operator, where h and are the step sizes in space and time, respectively. At the same time, the optimal convergence rates in time and space for the nonconforming scheme are also investigated by some special characters of nonconforming element, which manifests that convergence orders of and for the original variable u in broken -norm and -norm, respectively, and approximation for the flux converging with order in -norm. Numerical examples are provided to demonstrate the theoretical analysis. |
| 资助项目 | National Natural Science Foundation of China[11101381] ; National Natural Science Foundation of China[11371357] ; Outstanding Young Talents Training Plan by Xuchang University |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000391930500017 |
| 出版者 | SPRINGER/PLENUM PUBLISHERS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/24563]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Tang, Yifa |
| 作者单位 | 1.Xuchang Univ, Sch Math & Stat, Xuchang 461000, Peoples R China 2.Huainan Vocat & Tech Coll, Div Basic Educ, Huainan 232001, Peoples R China 3.Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China 4.Cipher Ground, 675 Rt 1 South, North Brunswick, NJ 08902 USA 5.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhao, Yanmin,Chen, Pan,Bu, Weiping,et al. Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations[J]. JOURNAL OF SCIENTIFIC COMPUTING,2017,70(1):407-428. |
| APA | Zhao, Yanmin,Chen, Pan,Bu, Weiping,Liu, Xiangtao,&Tang, Yifa.(2017).Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations.JOURNAL OF SCIENTIFIC COMPUTING,70(1),407-428. |
| MLA | Zhao, Yanmin,et al."Two Mixed Finite Element Methods for Time-Fractional Diffusion Equations".JOURNAL OF SCIENTIFIC COMPUTING 70.1(2017):407-428. |
入库方式： OAI收割
来源：数学与系统科学研究院
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