H<mml:msup>2</mml:msup>-Korn's Inequality and the Nonconforming Elements for The Strain Gradient Elastic Model

doi:10.1007/s10915-021-01597-7

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	H2-Korn's Inequality and the Nonconforming Elements for The Strain Gradient Elastic Model
	Li, Hongliang 1; Ming, Pingbing 2,3; Wang, Huiyu 4
	2021-09-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	88 期号:3 页码:23
摘要	We establish a new H2-Korn's inequality and its discrete analog, which greatly simplify the construction of nonconforming elements for a linear strain gradient elastic model. The Specht triangle (Specht in Int J Numer Methods Eng 28:705-715, 1988) and the NZT tetrahedron (Wang et al. in Numer Math 106:335-347, 2007) are analyzed as two typical representatives for robust nonconforming elements in the sense that the rate of convergence is independent of the small material parameter. We construct the regularized interpolation operators and the enriching operators for both elements, and prove the error estimates under minimal smoothness assumption on the solution. Numerical results for the smooth solution, and the solution with boundary layer are consistent with the corresponding theoretical prediction.
关键词	Strain gradient elasticity H2-Korn's Robust finite elements
DOI	10.1007/s10915-021-01597-7
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11971467] ; Beijing Academy of Artificial Intelligence (BAAI)
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000692355900001
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59209
专题	中国科学院数学与系统科学研究院
通讯作者	Ming, Pingbing
作者单位	1.Sichuan Normal Univ, Sch Math & Sci, Chengdu 610066, Peoples R China 2.AMSS Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, LSEC, 55 East Rd Zhong Guan Cun, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Beijing 101 Middle Sch, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Li, Hongliang,Ming, Pingbing,Wang, Huiyu. H2-Korn's Inequality and the Nonconforming Elements for The Strain Gradient Elastic Model[J]. JOURNAL OF SCIENTIFIC COMPUTING,2021,88(3):23.
APA	Li, Hongliang,Ming, Pingbing,&Wang, Huiyu.(2021).H2-Korn's Inequality and the Nonconforming Elements for The Strain Gradient Elastic Model.JOURNAL OF SCIENTIFIC COMPUTING,88(3),23.
MLA	Li, Hongliang,et al."H2-Korn's Inequality and the Nonconforming Elements for The Strain Gradient Elastic Model".JOURNAL OF SCIENTIFIC COMPUTING 88.3(2021):23.