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Artículo científico (article).
On numerical regularity of the face-to-face longest-edge bisection algorithm for tetrahedral partitions
BIRD. BCAM's Institutional Repository Data
oai:bird.bcamath.org:20.500.11824/113
BIRD. BCAM's Institutional Repository Data
- Hannukainen, A.
- Korotov, S.
- Krizek, M.
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.
DOI: http://hdl.handle.net/20.500.11824/113
BIRD. BCAM's Institutional Repository Data
oai:bird.bcamath.org:20.500.11824/113
HANDLE: http://hdl.handle.net/20.500.11824/113
BIRD. BCAM's Institutional Repository Data
oai:bird.bcamath.org:20.500.11824/113
Ver en: http://hdl.handle.net/20.500.11824/113
BIRD. BCAM's Institutional Repository Data
oai:bird.bcamath.org:20.500.11824/113
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BIRD. BCAM's Institutional Repository Data
oai:bird.bcamath.org:20.500.11824/113
Artículo científico (article). 2014
ON NUMERICAL REGULARITY OF THE FACE-TO-FACE LONGEST-EDGE BISECTION ALGORITHM FOR TETRAHEDRAL PARTITIONS
BIRD. BCAM's Institutional Repository Data
- Hannukainen, A.
- Korotov, S.
- Krizek, M.
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.
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