Semiregular Hermite tetrahedral finite elements.
type: Item
instance of: scholarly article
title: Semiregular Hermite tetrahedral finite elements.
zbMATH Open document ID: 1066.65118
DOI: 10.1023/A:1013700225774
author: Alexander Ženíšek
author: Jana Hoderová-Zlámalová
published in: Applications of Mathematics
publication date: 2005-04-19T00:00:00Z
full work available at URL: https://eudml.org/doc/33088
review text: The authors examine tetrahedral Hermite \(C^0\)-elements satisfying the maximum angle condition. They introduce the notion ``a semiregular tetrahedron'', which is characterized as follows: There exists a constant \(\omega _0 < \pi \) such that the inner angle between its arbitrary two faces is less than or equal \(\omega _0\). Three basic manners, in which semiregular tetrahedra may degenerate, are described. Further, special degrees of freedom of semiregular tetrahedral Hermite elements are defined to get the best interpolation properties of these finite elements. Several new interpolation theorems are proved. They are applied to finite element approximation of the Poisson equation with mixed boundary conditions on a bounded polyhedral domain. The rate of convergence \(O(h^{3-\varepsilon })\) in \(H^1\)-norm is derived for any \(\varepsilon > 0\).
reviewed by: Michal Křížek
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 2158711
zbMATH Keywords: tetrahedral Hermite finite elements
zbMATH Keywords: maximum angle condition
zbMATH Keywords: interpolation
zbMATH Keywords: Poisson equation
zbMATH Keywords: convergence
MaRDI profile type: Publication
cites work: Anisotropic interpolation with applications to the finite element method
cites work: On the Angle Condition in the Finite Element Method
cites work: Sard kernel theorems on triangular domains with application to finite element error bounds
cites work: Error estimates for 3-d narrow finite elements
cites work: Q4116016
cites work: On semiregular families of triangulations and linear interpolation
cites work: On the Maximum Angle Condition for Linear Tetrahedral Elements
cites work: Uniform Error Estimates for Certain Narrow Lagrange Finite Elements
cites work: Q3243480
cites work: Q3998714
cites work: Maximum-Angle Condition and Triangular Finite Elements of Hermite Type
cites work: On the finite element method
OpenAlex ID: W54660289
description: scientific article; zbMATH DE number 2158711