Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems

doi:10.1093/imanum/drz029

CSpace

	Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems
	Gong, Wei 1,2; Li, Buyang 3
	2020-10-01
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	40 期号:4 页码:2898-2939
摘要	The parabolic Dirichlet boundary control problem and its finite element discretization are considered in convex polygonal and polyhedral domains. We improve the existing results on the regularity of the solutions by establishing and utilizing the maximal L-p-regularity of parabolic equations under inhomogeneous Dirichlet boundary conditions. Based on the proved regularity of the solutions, we prove O(h(1-1)/q(0-epsilon)) convergence for the semidiscrete finite element solutions for some q(0) > 2, with q(0) depending on the maximal interior angle at the corners and edges of the domain and epsilon being a positive number that can be arbitrarily small.
关键词	Dirichlet boundary control parabolic equation finite element method maximal L-p-regularity
DOI	10.1093/imanum/drz029
收录类别	SCI
语种	英语
资助项目	Key Research Program of the Chinese Academy of Sciences[XDPB11] ; National Key Basic Research Program[2018YFB0704304] ; National Natural Science Foundation of China[11671391] ; National Natural Science Foundation of China[91530204] ; Research Grant Council of Hong Kong[15301818]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000610489200025
出版者	OXFORD UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58062
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Buyang
作者单位	1.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Natl Ctr Math & Interdisciplinary Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Gong, Wei,Li, Buyang. Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2020,40(4):2898-2939.
APA	Gong, Wei,&Li, Buyang.(2020).Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems.IMA JOURNAL OF NUMERICAL ANALYSIS,40(4),2898-2939.
MLA	Gong, Wei,et al."Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems".IMA JOURNAL OF NUMERICAL ANALYSIS 40.4(2020):2898-2939.