A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials

doi:10.1007/s10092-021-00447-0

CSpace

	A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials
	Quan, Qimeng 1; Ji, Xia 2,3; Zhang, Shuo 4,5
	2022-03-01
发表期刊	CALCOLO
ISSN	0008-0624
卷号	59 期号:1 页码:32
摘要	This paper discusses finite elements defined by Ciarlet's triple on grids that consist of general quadrilaterals not limited in parallelograms. Specifically, two finite elements are established for the H-1 and H (rot) elliptic problems, respectively. An O(h) order convergence rate in energy norm for both of them and an O(h(2)) order convergence in L-2 norm for the H-1 scheme are proved under the O(h(2)) asymptotic-parallelogram assumption on the grids. Further, these two finite element spaces, together with the space of piecewise constant functions, formulate a discretized de Rham complex on general quadrilateral grids. The finite element spaces consist of piecewise polynomial functions, and, thus, are nonconforming on general quadrilateral grids. Indeed, a rigorous analysis is given in this paper that it is impossible to construct a practically useful finite element by Ciarlet's triple that can formulate a finite element space which consists of continuous piecewise polynomial functions on a grid that may include arbitrary quadrilaterals.
关键词	Nonconforming finite element De Rham complex General quadrilateral grids Piecewise polynomial
DOI	10.1007/s10092-021-00447-0
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11871465] ; National Natural Science Foundation of China[11471026] ; Beijing Natural Science Foundation[Z200003] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDB 41000000]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000727851500001
出版者	SPRINGER-VERLAG ITALIA SRL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59677
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Shuo
作者单位	1.Univ Chinese Acad Sci, Beijing 100190, Peoples R China 2.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China 3.Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 100081, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Quan, Qimeng,Ji, Xia,Zhang, Shuo. A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials[J]. CALCOLO,2022,59(1):32.
APA	Quan, Qimeng,Ji, Xia,&Zhang, Shuo.(2022).A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials.CALCOLO,59(1),32.
MLA	Quan, Qimeng,et al."A lowest-degree quasi-conforming finite element de Rham complex on general quadrilateral grids by piecewise polynomials".CALCOLO 59.1(2022):32.