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High Order Mass-Lumping Finite Elements on Simplexes
Cui, Tao1; Leng, Wei1; Lin, Deng1,2; Ma, Shichao1,2; Zhang, Linbo1,2
AbstractThis 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.
KeywordFinite element mass-lumping simplex numerical quadrature multivariate polynomial interpolation unisolvence
Funding ProjectNational 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 AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000400931100008
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Document Type期刊论文
Corresponding AuthorZhang, Linbo
Affiliation1.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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