High Order Mass-Lumping Finite Elements on Simplexes

doi:10.4208/nmtma.2017.s07

	High Order Mass-Lumping Finite Elements on Simplexes
	Cui, Tao1 ; Leng, Wei1 ; Lin, Deng 1,2; Ma, Shichao 1,2; Zhang, Linbo1,2
	2017-05-01
发表期刊	NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
ISSN	1004-8979
卷号	10 期号:2 页码:331-350
摘要	This paper is concerned with the construction of high order mass-lumping finite elements on simplexes and a program for computing mass-lumping finite elements on triangles and tetrahedra. The polynomial spaces for mass-lumping finite elements, as proposed in the literature, are presented and discussed. In particular, the unisolvence problem of symmetric point-sets for the polynomial spaces used in mass-lumping elements is addressed, and an interesting property of the unisolvent symmetric point-sets is observed and discussed. Though its theoretical proof is still lacking, this property seems to be true in general, and it can greatly reduce the number of cases to consider in the computations of mass-lumping elements. A program for computing mass-lumping finite elements on triangles and tetrahedra, derived from the code for computing numerical quadrature rules presented in [7], is introduced. New mass-lumping finite elements on triangles found using this program with higher orders, namely 7, 8 and 9, than those available in the literature are reported.
关键词	Finite element mass-lumping simplex numerical quadrature multivariate polynomial interpolation unisolvence
DOI	10.4208/nmtma.2017.s07
语种	英语
资助项目	National Key Research and Development Program[2016YFB0201304] ; China NSF[91430215] ; China NSF[91530323] ; China NSF[11321061] ; State Key Laboratory of Scientific and Engineering Computing (LSEC) ; National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences (NCMIS)
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000400931100008
出版者	CAMBRIDGE UNIV 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/25397
专题	计算数学与科学工程计算研究所
通讯作者	Zhang, Linbo
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, 55 East Zhongguancun Rd, 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	Cui, Tao,Leng, Wei,Lin, Deng,et al. High Order Mass-Lumping Finite Elements on Simplexes[J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,2017,10(2):331-350.
APA	Cui, Tao,Leng, Wei,Lin, Deng,Ma, Shichao,&Zhang, Linbo.(2017).High Order Mass-Lumping Finite Elements on Simplexes.NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS,10(2),331-350.
MLA	Cui, Tao,et al."High Order Mass-Lumping Finite Elements on Simplexes".NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS 10.2(2017):331-350.