Red refinements of simplices into congruent subsimplices

0430376 - MÚ 2015 RIV GB eng J - Journal Article
Korotov, S. - Křížek, Michal
Red refinements of simplices into congruent subsimplices.
Computers & Mathematics With Applications. Roč. 67, č. 12 (2014), s. 2199-2204. ISSN 0898-1221. E-ISSN 1873-7668
R&D Projects: GA ČR GA14-02067S
Institutional support: RVO:67985840
Keywords : sommerville tetrahedron * red refinement * higher-dimensional simplex
Subject RIV: BA - General Mathematics
Impact factor: 1.697, year: 2014
http://www.sciencedirect.com/science/article/pii/S0898122114000662

We show that in dimensions higher than two, the popular "red refinement" technique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which are all acute even for an acute father element as opposed to the two-dimensional case. In the three-dimensional case we prove that there exists only one tetrahedron that can be partitioned by red refinement into eight congruent subtetrahedra that are all similar to the original one.
Permanent Link: http://hdl.handle.net/11104/0235320