An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations

doi:10.1007/s11425-020-1882-6

CSpace

	An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations
	Zhang, Shuo 1,2
	2021-08-12
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
页码	24
摘要	This paper presents a nonconforming finite element scheme for the planar biharmonic equation, which applies piecewise cubic polynomials (P-3) and possesses O(h(2)) convergence rate for smooth solutions in the energy norm on general shape-regular triangulations. Both Dirichlet and Navier type boundary value problems are studied. The basis for the scheme is a piecewise cubic polynomial space, which can approximate the H-4 functions with O(h(2)) accuracy in the broken H-2 norm. Besides, a discrete strengthened Miranda-Talenti estimate (del(2)(h) center dot, del(2)(h) center dot) = (Delta(h) center dot, Delta h center dot), which is usually not true for nonconforming finite element spaces, is proved. The finite element space does not correspond to a finite element defined with Ciarlet's triple; however, it admits a set of locally supported basis functions and can thus be implemented by the usual routine. The notion of the finite element Stokes complex plays an important role in the analysis as well as the construction of the basis functions.
关键词	biharmonic equation optimal cubic finite element scheme general triangulation discretized Stokes complex discrete strengthened Miranda-Talenti estimate
DOI	10.1007/s11425-020-1882-6
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] ; 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:000684493900002
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59060
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.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Shuo. An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations[J]. SCIENCE CHINA-MATHEMATICS,2021:24.
APA	Zhang, Shuo.(2021).An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations.SCIENCE CHINA-MATHEMATICS,24.
MLA	Zhang, Shuo."An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations".SCIENCE CHINA-MATHEMATICS (2021):24.