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

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 partiti...

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Veröffentlicht in:Science of computer programming Jg. 90; S. 34 - 41
Hauptverfasser: Hannukainen, Antti, Korotov, Sergey, Křížek, Michal
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 15.09.2014
Schlagworte:
Bisection algorithm
Conforming finite element method
Nested tetrahedral partitions
Regular family of partitions
Simplicial elements
Bisection algorithm
Simplicial elements
Conforming finite element method
Nested tetrahedral partitions
Regular family of partitions
ISSN:0167-6423, 1872-7964
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Zusammenfassung: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. •We examine the longest-edge bisection algorithm that refines simplicial partitions.•The resulting families of partitions are regular iff they are strongly regular.•The longest-edge bisection algorithm is very easy to implement in any dimension.•Numerical tests seem to produce regular families of tetrahedral partitions.
ISSN:0167-6423
1872-7964
DOI:10.1016/j.scico.2013.05.002