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Article

Korotov, Sergey ; Křížek, Michal
On simplicial red refinement in three and higher dimensions. (English). In: Brandts, J., Korotov, S., Křížek, M., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2013, In honor of the 70th birthday of Karel Segeth. Proceedings. Prague, May 15-17, 2013. Institute of Mathematics AS CR, Prague, 2013. pp. 131-139
MSC: 51M20, 52B11, 65N30, 65N50 | MR 3204438 | Zbl 1340.65271
Keywords:
red refinement; acute simplex; higher dimensional; tetrahedron; finite element meshes
Summary:
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.
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