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• W2073259706 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 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. • 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." @default.
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• W2073259706 date "2014-09-01" @default.
• W2073259706 modified "2023-10-18" @default.
• W2073259706 title "On numerical regularity of the face-to-face longest-edge bisection algorithm for tetrahedral partitions" @default.
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• W2073259706 doi "https://doi.org/10.1016/j.scico.2013.05.002" @default.
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