On numerical regularity of the face-to-face longest-edge bisection algorithm for tetrahedral partitions

0428478 - MÚ 2015 RIV NL eng J - Journal Article
Hannukainen, A. - Korotov, S. - Křížek, Michal
On numerical regularity of the face-to-face longest-edge bisection algorithm for tetrahedral partitions.
Science of Computer Programming. Roč. 90, Part A (2014), s. 34-41. ISSN 0167-6423. E-ISSN 1872-7964
R&D Projects: GA ČR GA14-02067S
Institutional support: RVO:67985840
Keywords : bisection algorithm * conforming finite element method * regular family of partitions
Subject RIV: BA - General Mathematics
Impact factor: 0.715, year: 2014
http://www.sciencedirect.com/science/article/pii/S0167642313001226

The finite element method usually requires regular or strongly regular families of partitions in order to get guaranteed a priori or a posteriori error estimates. In this paper we examine the recently invented longest-edge bisection algorithm that always produces only face-to-face simplicial partitions. First, we prove that the regularity of the family of partitions generated by this algorithm is equivalent to its strong regularity in any dimension. Second, we present a number of 3 d numerical tests, which demonstrate that the technique seems to produce regular (and therefore strongly regular) families of tetrahedral partitions. However, a mathematical proof of this statement is still an open problem.
Permanent Link: http://hdl.handle.net/11104/0233821