STOCHASTIC CONVERGENCE OF REGULARIZED SOLUTIONS AND THEIR FINITE ELEMENT APPROXIMATIONS TO INVERSE SOURCE PROBLEMS

doi:10.1137/21M1409779

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	STOCHASTIC CONVERGENCE OF REGULARIZED SOLUTIONS AND THEIR FINITE ELEMENT APPROXIMATIONS TO INVERSE SOURCE PROBLEMS
	CHEN, Z. H. I. M. I. N. G.1,2; ZHANG, W. E. N. L. O. N. G.3; ZOU, J. U. N.4
	2022
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	60 期号:2 页码:751-780
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.
关键词	inverse source problems regularization finite element approximation stochastic error estimates
DOI	10.1137/21M1409779
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000813362600010
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61251
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.