WHITNEY FORMS OF HIGHER DEGREE

被引：47
|
作者：
Rapetti, Francesca [1 ,2 ]
Bossavit, Alain [3 ,4 ]
机构：
[1] CNRS, UMR 6621, Math Lab, F-06108 Nice 02, France
[2] Univ Nice & Sophia Antipolis, F-06108 Nice 02, France
[3] CNRS, UMR 8507, Lab Genie Elect Paris, F-91192 Gif Sur Yvette, France
[4] Univ Supelec, F-91192 Gif Sur Yvette, France
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2009年 / 47卷 / 03期
关键词：
Whitney forms; simplicial meshes; high-order approximations; FINITE-ELEMENTS; HIGHER-ORDER; TETRAHEDRA; BASES;
D O I：
10.1137/070705489
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Low-order Whitney elements are widely used for electromagnetic field problems. Higher-order approximations are receiving increasing interest, but their definition remains unduly complex. In this paper we propose a new simple construction for Whitney p-elements of polynomial degree higher than one that use only degrees of freedom associated to p-chains. We provide a basis for these elements on simplicial meshes and give a geometrical localization of all degrees of freedom. Properties of the higher-order Whitney complex are deeply investigated.
引用
收藏
页码：2369 / 2386
页数：18
相关论文
共 50 条
  • [31] Diagonalizable higher degree forms and symmetric tensors
    Huang, Hua-Lin
    Lu, Huajun
    Ye, Yu
    Zhang, Chi
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 613 : 151 - 169
  • [32] Forms of higher degree over certain fields
    Glazman A.L.
    Zatitski P.B.
    Sivatski A.S.
    Stolyarov D.M.
    Journal of Mathematical Sciences, 2013, 188 (5) : 591 - 595
  • [33] Whitney forms and their extensions
    Lohi, Jonni
    Kettunen, Lauri
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 393
  • [34] On the invariants of differential forms of degree higher than two
    Haskins, Charles Nelson
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1903, 4 (1-4) : 38 - 43
  • [35] LOCAL GLOBAL THEOREMS FOR DIAGONAL FORMS OF HIGHER DEGREE
    BECKER, E
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1980, 318 : 36 - 50
  • [36] NORM PRINCIPLES FOR FORMS OF HIGHER DEGREE PERMITTING COMPOSITION
    Fitzgerald, R. W.
    Pumpluen, S.
    COMMUNICATIONS IN ALGEBRA, 2009, 37 (11) : 3851 - 3860
  • [37] Skew-holomorphic Jacobi forms of higher degree
    Hayashida, S
    Automorphic Forms and Zeta Functions, 2006, : 130 - 139
  • [38] NONDEGENERATE HIGHER DEGREE FORMS OVER DEDEKIND DOMAINS
    COLEMAN, DB
    CUNNINGHAM, J
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 52 (OCT) : 65 - 68
  • [39] On centres and direct sum decompositions of higher degree forms
    Huang, Hua-Lin
    Lu, Huajun
    Ye, Yu
    Zhang, Chi
    LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (22): : 7290 - 7306
  • [40] Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus
    Jonni Lohi
    Numerical Algorithms, 2022, 91 : 1261 - 1285
12345