On simplicial red refinement in three and higher dimensions

0392421 - MÚ 2014 RIV CZ eng C - Conference Paper (international conference)
Korotov, S. - Křížek, Michal
On simplicial red refinement in three and higher dimensions.
Applications of Mathematics 2013. Praha: Matematický ústav AV ČR, v.v.i, 2013 - (Brandts, S.; Korotov, S.; Křížek, M.; Šístek, J.; Vejchodský, T.), s. 131-139. ISBN 978-80-85823-61-5.
[Applications of Mathematics 2013. Prague (CZ), 15.05.2013-18.05.2013]
Institutional support: RVO:67985840
Keywords : red refinement * finite element analysis
Subject RIV: BA - General Mathematics
http://www.math.cas.cz/~am2013/proceedings/contributions/korotov.pdf

We show that in dimensions higher than two, the popular “red refinement” tech- nique, 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/11104/0221291