Optimal quadratic element on rectangular grids for H-1 problems

doi:10.1007/s10543-020-00821-4

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	Optimal quadratic element on rectangular grids for H-1 problems
	Zeng, Huilan 1,2; Zhang, Chen-Song 1,2; Zhang, Shuo 1,2
刊名	BIT NUMERICAL MATHEMATICS
	2020-08-26
页码	25
关键词	Optimal quadratic element Rectangular grids Boundary value problem Eigenvalue problem Lower bound
ISSN号	0006-3835
DOI	10.1007/s10543-020-00821-4
英文摘要	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.
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
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000563160100001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52033]
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, NCMIS, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, 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.