Nonstandard finite element de Rham complexes on cubical meshes

doi:10.1007/s10543-019-00779-y

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	Nonstandard finite element de Rham complexes on cubical meshes
	Gillette, Andrew 1; Hu, Kaibo 2; Zhang, Shuo 3,4
	2020-06-01
发表期刊	BIT NUMERICAL MATHEMATICS
ISSN	0006-3835
卷号	60 期号:2 页码:373-409
摘要	Two general operations are proposed on finite element differential complexes on cubical meshes that can be used to construct and analyze sequences of "nonstandard" convergent methods. The first operation, called DoF-transfer, moves edge degrees of freedom to vertices in a way that reduces global degrees of freedom while increasing continuity order at vertices. The second operation, called serendipity, eliminates interior bubble functions and degrees of freedom locally on each element without affecting edge degrees of freedom. These operations can be used independently or in tandem to create nonstandard complexes that incorporate Hermite, Adini and "trimmed-Adini" elements. The resulting elements lead to convergent non-conforming methods for problems requiring stronger regularity and satisfy a discrete Korn inequality. Potential benefits of applying these elements to Stokes, biharmonic and elasticity problems are discussed.
关键词	Finite element Nonconforming element de Rham complex
DOI	10.1007/s10543-019-00779-y
收录类别	SCI
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000537469000005
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51567
专题	中国科学院数学与系统科学研究院
通讯作者	Hu, Kaibo
作者单位	1.Univ Arizona, Dept Math, 617 N Santa Rita Ave, Tucson, AZ 85721 USA 2.Univ Minnesota, Sch Math, 206 Church St SE, Minneapolis, MN 55455 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Natl Ctr Math & Interdisciplinary Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Gillette, Andrew,Hu, Kaibo,Zhang, Shuo. Nonstandard finite element de Rham complexes on cubical meshes[J]. BIT NUMERICAL MATHEMATICS,2020,60(2):373-409.
APA	Gillette, Andrew,Hu, Kaibo,&Zhang, Shuo.(2020).Nonstandard finite element de Rham complexes on cubical meshes.BIT NUMERICAL MATHEMATICS,60(2),373-409.
MLA	Gillette, Andrew,et al."Nonstandard finite element de Rham complexes on cubical meshes".BIT NUMERICAL MATHEMATICS 60.2(2020):373-409.