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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| Published in: | Science of computer programming Vol. 90; pp. 34 - 41 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
15.09.2014
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| Subjects: | |
| ISSN: | 0167-6423, 1872-7964 |
| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 0167-6423 1872-7964 |
| DOI: | 10.1016/j.scico.2013.05.002 |