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

Antti Hannukainen, Sergey Korotov*, Michal Křížek

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)

Abstract

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 3d 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.

Original languageEnglish
Pages (from-to)34-41
Number of pages8
JournalScience of Computer Programming
Volume90
Issue numberPART A
DOIs
Publication statusPublished - 15 Sep 2014
MoE publication typeA1 Journal article-refereed

Keywords

  • Bisection algorithm
  • Conforming finite element method
  • Nested tetrahedral partitions
  • Regular family of partitions
  • Simplicial elements

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