On Nonobtuse Simplicial Partitions

Abstract

On nonobtuse simplicial partitionsBrandts, J.H.; Korotov, S.; Kížek, M.; Šolc, J. Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Download date: 10 May 2018Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. Dedicated to Ivan Hlaváček on his 75th birthdayAbstract. This paper surveys some results on acute and nonobtuse simplices and associated spatial partitions. These partitions are relevant in numerical mathematics, including piecewise polynomial approximation theory and the finite element method. Special attention is paid to a basic type of nonobtuse simplices called path-simplices, the generalization of right triangles to higher dimensions. In addition to applications in numerical mathematics, we give examples of the appearance of acute and nonobtuse simplices in other areas of mathematics.

Discrete nonnegativity for nonlinear cooperative parabolic PDE systems with non-monotone coupling

“…on acute simplicial meshes if linear finite elements are used in the space discretization [8]. The issue of generation of such meshes is considered in [1,4,14] and references therein.…”

Finite element approximation of finitely extensible nonlinear elastic dumbbell models for dilute polymers

“…For the construction of nonobtuse three-dimensional simplicial partitions we refer to the papers of Korotov and Křížek [22,23] for example; the reader should note, however, that in [22] the authors use the term acute when they mean nonobtuse. Elsewhere in the computational geometry literature the term acute is reserved for a simplicial partition where all dihedral angles of any simplex in the partition are <π/2, which is a more restrictive requirement (especially in the case of d = 3) than what we assume here; see, for example, the articles of Brandts et al [11], Eppstein et al [16], and Itoh and Zamfirescu [18], and references therein. Nonobtuse simplicial partitions are sometimes also called weakly acute (cf.…”

Finite element approximation of kinetic dilute polymer models with microscopic cut-off

“…For the construction of nonobtuse three-dimensional simplicial partitions we refer to the papers of Korotov and Krížek [28,29] for example; the reader should note, however, that in [28] the authors use the term acute when they mean nonobtuse. Elsewhere in the computational geometry literature the term acute is reserved for a simplicial partition where all dihedral angles of any simplex in the partition are < π/2, which is a more restrictive requirement (especially in the case of d = 3) than what we assume here; see, for example, the articles of Brandts et al [10], Eppstein et al [20], and Itoh and Zamfirescu [23], and references therein. Nonobtuse simplicial partitions are sometimes also called weakly acute (cf.…”