KMS Of Academy of mathematics and systems sciences, CAS
High Order Mass-Lumping Finite Elements on Simplexes | |
Cui, Tao1; Leng, Wei1; Lin, Deng1,2; Ma, Shichao1,2; Zhang, Linbo1,2 | |
2017-05-01 | |
Source Publication | NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS |
ISSN | 1004-8979 |
Volume | 10Issue:2Pages:331-350 |
Abstract | 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. |
Keyword | Finite element mass-lumping simplex numerical quadrature multivariate polynomial interpolation unisolvence |
DOI | 10.4208/nmtma.2017.s07 |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000400931100008 |
Publisher | CAMBRIDGE UNIV PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/25397 |
Collection | 计算数学与科学工程计算研究所 |
Corresponding Author | Zhang, Linbo |
Affiliation | 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 |
Recommended Citation 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. |
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