STOCHASTIC CONVERGENCE OF REGULARIZED SOLUTIONS AND THEIR FINITE ELEMENT APPROXIMATIONS TO INVERSE SOURCE PROBLEMS
文献类型：期刊论文
| 作者 | CHEN, Z. H. I. M. I. N. G.1,2; ZHANG, W. E. N. L. O. N. G.3; ZOU, J. U. N.4 |
| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2022 |
| 卷号 | 60期号:2页码:751-780 |
| 关键词 | inverse source problems regularization finite element approximation stochastic error estimates |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/21M1409779 |
| 英文摘要 | In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and we establish the stochastic convergence and optimal finite element convergence rates of these solutions under point-wise measurement data with random noise. The regularization error estimates and the finite element error estimates are derived with explicit dependence on the noise level, regularization parameter, mesh size, and time step size, which can guide practical choices among these key parameters in real applications. The error estimates also suggest an iterative algorithm for determining an optimal regularization parameter. Numerical experiments are presented to demonstrate the effectiveness of the analytical results. |
| 资助项目 | China National Key Technologies RD Program[2019YFA0709600] ; Shenzhen SciTech Fund[RCBS20200714114941241] ; National Natural Science Foundation of China[11901282] ; National Natural Science Foundation of China[118311061] ; Hong Kong RGC General Research Fund[14306719] ; Hong Kong RGC General Research Fund[14306718] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000813362600010 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/61250]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | CHEN, Z. H. I. M. I. N. G. |
| 作者单位 | 1.Chinese Acad Sci, LSEC, Inst Computat Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China 3.Southern Univ Sci & Technol SUSTech, Dept Math, Shenzhen, Guangdong, Peoples R China 4.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China |
| 推荐引用方式 GB/T 7714 | CHEN, Z. H. I. M. I. N. G.,ZHANG, W. E. N. L. O. N. G.,ZOU, J. U. N.. STOCHASTIC CONVERGENCE OF REGULARIZED SOLUTIONS AND THEIR FINITE ELEMENT APPROXIMATIONS TO INVERSE SOURCE PROBLEMS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2022,60(2):751-780. |
| APA | CHEN, Z. H. I. M. I. N. G.,ZHANG, W. E. N. L. O. N. G.,&ZOU, J. U. N..(2022).STOCHASTIC CONVERGENCE OF REGULARIZED SOLUTIONS AND THEIR FINITE ELEMENT APPROXIMATIONS TO INVERSE SOURCE PROBLEMS.SIAM JOURNAL ON NUMERICAL ANALYSIS,60(2),751-780. |
| MLA | CHEN, Z. H. I. M. I. N. G.,et al."STOCHASTIC CONVERGENCE OF REGULARIZED SOLUTIONS AND THEIR FINITE ELEMENT APPROXIMATIONS TO INVERSE SOURCE PROBLEMS".SIAM JOURNAL ON NUMERICAL ANALYSIS 60.2(2022):751-780. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。