On numerical regularity of the face-to-face longest-edge bisection algorithm for tetrahedral partitions - Hannukainen, Antti; Korotov, Sergey; Křížek, Michal (Science of computer programming, 2014)
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.