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@article{SJVM_2021_24_4_a3,
author = {S. Korotov and M. K\v{r}{\'\i}\v{z}ek},
title = {On degenerating tetrahedra resulting from red refinements of tetrahedral partitions},
journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
pages = {383--392},
publisher = {mathdoc},
volume = {24},
number = {4},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SJVM_2021_24_4_a3/}
}
TY - JOUR AU - S. Korotov AU - M. Křížek TI - On degenerating tetrahedra resulting from red refinements of tetrahedral partitions JO - Sibirskij žurnal vyčislitelʹnoj matematiki PY - 2021 SP - 383 EP - 392 VL - 24 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SJVM_2021_24_4_a3/ LA - ru ID - SJVM_2021_24_4_a3 ER -
%0 Journal Article %A S. Korotov %A M. Křížek %T On degenerating tetrahedra resulting from red refinements of tetrahedral partitions %J Sibirskij žurnal vyčislitelʹnoj matematiki %D 2021 %P 383-392 %V 24 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/SJVM_2021_24_4_a3/ %G ru %F SJVM_2021_24_4_a3
S. Korotov; M. Křížek. On degenerating tetrahedra resulting from red refinements of tetrahedral partitions. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 4, pp. 383-392. http://geodesic.mathdoc.fr/item/SJVM_2021_24_4_a3/
[1] Babuska I., Aziz A. K., “On the angle condition in the finite element method”, SIAM J. Numer. Anal., 13 (1976), 214–226
[2] Baidakova N. V., “On Jamet's estimates for the finite element method with interpolation at uniform nodes of a simplex”, Sib. Adv. Math., 28 (2018), 1–22
[3] Bey J., “Simplicial grid refinement: on Freudenthal's algorithm and the optimal number of congruence classes”, Numer. Math., 85 (2000), 1–29
[4] Brandts J., Korotov S., Krizek M., Simplicial Partitions with Applications to the Finite Element Method, Springer-Verlag, Berlin, 2020
[5] Ciarlet P. G., The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978
[6] Edelsbrunner H., “Triangulations and meshes in computational geometry”, Acta Numer., 9 (2000), 133–213
[7] Grande J., “Red-green refinement of simplicial meshes in $d$ dimensions”, Math. Comp., 88 (2019), 751–782
[8] Jamet P., “Estimations d'erreur pour des elements finis droits presque degeneres”, RAIRO Anal. Numer., 10 (1976), 43–60
[9] Khademi A., Korotov S., Vatne J. E., “On generalizations of the Synge- Kr?zek maximum angle condition for d-simplices”, J. Comput. Appl. Math., 358 (2019), 29–33
[10] Korotov S., Krizek M., “Red refinements of simplices into congruent subsimplices”, Comput. Math. Appl., 67 (2014), 2199–2204
[11] Krizek M., “An equilibrium finite element method in three-dimensional elasticity”, Appl. Math., 27 (1982), 46–75
[12] Krizek M., “On the maximum angle condition for linear tetrahedral elements”, SIAM J. Numer. Anal., 29 (1992), 513–520
[13] Krizek M., Strouboulis T., “How to generate local refinements of unstructured tetrahedral meshes satisfying a regularity ball condition”, Numer. Methods for Partial Differential Equations, 13 (1997), 201–214
[14] Sommerville D. M.Y., “Division of space by congruent triangles and tetrahedra”, Proc. Royal Soc. Edinburgh, 43 (1923), 85–116
[15] Zenisek A., “Convergence of the finite element method for boundary value problems of a system of elliptic equations”, Appl. Math., 14 (1969), 355–377 (in Czech)
[16] Zenisek A., “Variational problems in domains with cusp points”, Appl. Math., 38 (1993), 381–403
[17] Zenisek A., Hoderova-Zlamalova J., “Semiregular Hermite tetrahedral finite elements”, Appl. Math., 46 (2001), 295–315
[18] Zhang S., “Successive subdivisions of tetrahedra and multigrid methods on tetrahedral meshes”, Houston J. Math., 21:2 (1995), 541–556