Global and local refinement techniques yielding nonobtuse tetrahedral partitions
type: Item
instance of: scholarly article
title: Global and local refinement techniques yielding nonobtuse tetrahedral partitions
zbMATH Open document ID: 1086.65116
publication date: 2006-02-16T00:00:00Z
review text: A tetrahedron is said to be a path tetrahedron if its three edges, which do not meet at the same vertex are mutually orthogonal. The authors state a set of conditions on a tetrahedron \( T \) which ensures the existence of a family of partitions of \( T \) consisting of path tetrahedrons only [see \textit{M. Krizek} and \textit{J. Pradlova}, Numer. Methods Partial Differ. Equations 16, 327--334 (2000; Zbl 0957.65012)]. Considering a path tetrahedron \( ABCD \) such that the edges \( AB, BC \) and \( CD \) are mutually orthogonal, the authors prove that there exists an infinite family of nonobtuse partitions of it into path tetrahedra that locally refine \( ABCD \) in a neighbourhood of the vertex \( A \).
reviewed by: H. P. Dikshit
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 5006948
zbMATH Keywords: nonobtuse tetrahedra
zbMATH Keywords: global and local refinements
zbMATH Keywords: elliptic equations
zbMATH Keywords: parabolic equations
zbMATH Keywords: discrete maximum principle
zbMATH Keywords: finite-element method
zbMATH Keywords: linear tetrahedral finite elements
author: Sergey Korotov
author: Michal Křížek
MaRDI profile type: Publication
full work available at URL: j.camwa.2005.08.012
OpenAlex ID: W2019236302
cites work: Acute type refinements of tetrahedral partitions of polyhedral domains
cites work: Comparison principle for a nonlinear parabolic problem of a nonmonotone type
cites work: Maximum principle and uniform convergence for the finite element method
cites work: Qualitative properties of the numerical solution of linear parabolic problems with nonhomogeneous boundary conditions
cites work: Finite-element solution of flow problems with trailing conditions
cites work: The maximum principle for bilinear elements
cites work: Q4151103
cites work: Q3890207
cites work: DISCRETE CONSERVATION AND DISCRETE MAXIMUM PRINCIPLE FOR ELLIPTIC PDEs
cites work: Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle
cites work: On a Maximum Principle for Matrices, and on Conservation of Monotonicity. With Applications to Discretization Methods
cites work: On maximum principles for monotone matrices
cites work: Q4838037
cites work: Q3996943
cites work: An equilibrium finite element method in three-dimensional elasticity
cites work: Q4867284
cites work: The generalized finite element method
cites work: Q4763371
cites work: Local mesh refinement in 2 and 3 dimensions
cites work: Q3123991
cites work: An approach to refining three‐dimensional tetrahedral meshes based on Delaunay transformations
cites work: Q4952860
cites work: Local nonobtuse tetrahedral refinements of a cube.
cites work: The dissection of a polygon into nearly equilateral triangles
DOI: 10.1016/J.CAMWA.2005.08.012
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 5006948