Optimal quadratic element on rectangular grids for H-1 problems

doi:10.1007/s10543-020-00821-4

	Optimal quadratic element on rectangular grids for H-1 problems
	Zeng, Huilan 1,2; Zhang, Chen-Song1,2 ; Zhang, Shuo1,2
	2020-08-26
发表期刊	BIT NUMERICAL MATHEMATICS
ISSN	0006-3835
页码	25
摘要	In this paper, a piecewise quadratic finite element method on rectangular grids for H-1 problems is presented. The proposed method can be viewed as a reduced rectangular Morley element. For the source problem, the convergence rate of this scheme is proved to be O(h(2)) in the energy norm on uniform grids over a convex domain. Alower bound of the L-2-norm error is also proved, which makes the capacity of this scheme more clear. For the eigenvalue problem, the computed eigenvalues by this element are shown to be the lower bounds of the exact ones. Some numerical results are presented to verify the theoretical findings.
关键词	Optimal quadratic element Rectangular grids Boundary value problem Eigenvalue problem Lower bound
DOI	10.1007/s10543-020-00821-4
收录类别	SCI
语种	英语
资助项目	National Key Research and Development Program, China[2016YFB0201304] ; Key Research Program of Frontier Sciences of CAS ; National Natural Science Foundation, China[11471026] ; National Natural Science Foundation, China[11871465]
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Mathematics, Applied
WOS记录号	WOS:000563160100001
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/52034
专题	计算数学与科学工程计算研究所
通讯作者	Zhang, Shuo
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zeng, Huilan,Zhang, Chen-Song,Zhang, Shuo. Optimal quadratic element on rectangular grids for H-1 problems[J]. BIT NUMERICAL MATHEMATICS,2020:25.
APA	Zeng, Huilan,Zhang, Chen-Song,&Zhang, Shuo.(2020).Optimal quadratic element on rectangular grids for H-1 problems.BIT NUMERICAL MATHEMATICS,25.
MLA	Zeng, Huilan,et al."Optimal quadratic element on rectangular grids for H-1 problems".BIT NUMERICAL MATHEMATICS (2020):25.