CONVERGENCE OF THE HIPTMAIR-XU PRECONDITIONER FOR MAXWELL'S EQUATIONS WITH JUMP COEFFICIENTS (I): EXTENSIONS OF THE REGULAR DECOMPOSITION

doi:10.1137/20M1320365

	CONVERGENCE OF THE HIPTMAIR-XU PRECONDITIONER FOR MAXWELL'S EQUATIONS WITH JUMP COEFFICIENTS (I): EXTENSIONS OF THE REGULAR DECOMPOSITION
	Hu, Qiya 1,2
刊名	SIAM JOURNAL ON NUMERICAL ANALYSIS
	2021
卷号	59 期号:5 页码:2500-2535
关键词	Maxwell's equations regular decomposition stability Nedelec elements
ISSN号	0036-1429
DOI	10.1137/20M1320365
英文摘要	This paper is the first in a series of two articles, aiming to prove the convergence of the HX preconditioner originally proposed by Hiptmair and Xu [SIAM T. Numer. Anal., 45 (2007), pp. 2483-2509] for Maxwell's equations with jump coefficients. In this paper, we establish several extensions of the discrete regular decomposition for edge finite element functions defined in three-dimensional domains. The functions defined by the new discrete regular decompositions can inherit zero degrees of freedom of the considered edge finite element function on some faces and edges of polyhedral domains as well as of some non-Lipschitz domains and possess nearly optimal stability with only a logarithmic factor.
资助项目	National Natural Science Foundation of China[G12071469]
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000752750400008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59998]
专题	中国科学院数学与系统科学研究院
通讯作者	Hu, Qiya
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Hu, Qiya. CONVERGENCE OF THE HIPTMAIR-XU PRECONDITIONER FOR MAXWELL'S EQUATIONS WITH JUMP COEFFICIENTS (I): EXTENSIONS OF THE REGULAR DECOMPOSITION[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2021,59(5):2500-2535.
APA	Hu, Qiya.(2021).CONVERGENCE OF THE HIPTMAIR-XU PRECONDITIONER FOR MAXWELL'S EQUATIONS WITH JUMP COEFFICIENTS (I): EXTENSIONS OF THE REGULAR DECOMPOSITION.SIAM JOURNAL ON NUMERICAL ANALYSIS,59(5),2500-2535.
MLA	Hu, Qiya."CONVERGENCE OF THE HIPTMAIR-XU PRECONDITIONER FOR MAXWELL'S EQUATIONS WITH JUMP COEFFICIENTS (I): EXTENSIONS OF THE REGULAR DECOMPOSITION".SIAM JOURNAL ON NUMERICAL ANALYSIS 59.5(2021):2500-2535.