On simplicial red refinement in three and higher dimensions

Korotov, Sergey, and Křížek, Michal. "On simplicial red refinement in three and higher dimensions." Applications of Mathematics 2013. Prague: Institute of Mathematics AS CR, 2013. 131-139. <http://eudml.org/doc/287856>.

@inProceedings{Korotov2013,
abstract = {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.},
author = {Korotov, Sergey, Křížek, Michal},
booktitle = {Applications of Mathematics 2013},
keywords = {red refinement; acute simplex; higher dimensional; tetrahedron; finite element meshes},
location = {Prague},
pages = {131-139},
publisher = {Institute of Mathematics AS CR},
title = {On simplicial red refinement in three and higher dimensions},
url = {http://eudml.org/doc/287856},
year = {2013},
}

TY - CLSWK
AU - Korotov, Sergey
AU - Křížek, Michal
TI - On simplicial red refinement in three and higher dimensions
T2 - Applications of Mathematics 2013
PY - 2013
CY - Prague
PB - Institute of Mathematics AS CR
SP - 131
EP - 139
AB - 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.
KW - red refinement; acute simplex; higher dimensional; tetrahedron; finite element meshes
UR - http://eudml.org/doc/287856
ER -