[Interpolation Brezzi–Douglas–Marini sur les simplexes et prismes anisotropes]
The Brezzi–Douglas–Marini interpolation error on anisotropic elements has been analyzed in two recent publications, the first focusing on simplices with estimates in , the other considering parallelotopes with estimates in terms of -norms. This contribution provides generalized estimates for anisotropic simplices for the case, , and shows new estimates for anisotropic prisms with triangular base.
L’erreur d’interpolation de Brezzi–Douglas–Marini sur les éléments anisotropes a été analysée dans deux publications récentes, la première se concentrant sur les simplices avec des estimations dans , l’autre considérant les parallelotopes avec des estimations en termes de normes . Notre contribution fournit des estimations généralisées pour les simplexes anisotropes pour le cas , , et montre de nouvelles estimations pour les prismes anisotropes à base triangulaire.
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Kempf, Volker 1
CC-BY 4.0
@article{CRMATH_2023__361_G1_437_0,
author = {Kempf, Volker},
title = {Brezzi{\textendash}Douglas{\textendash}Marini interpolation on anisotropic simplices and prisms},
journal = {Comptes Rendus. Math\'ematique},
pages = {437--443},
year = {2023},
publisher = {Acad\'emie des sciences, Paris},
volume = {361},
number = {G1},
doi = {10.5802/crmath.424},
language = {en},
url = {https://numdam.org/articles/10.5802/crmath.424/}
}
TY - JOUR AU - Kempf, Volker TI - Brezzi–Douglas–Marini interpolation on anisotropic simplices and prisms JO - Comptes Rendus. Mathématique PY - 2023 SP - 437 EP - 443 VL - 361 IS - G1 PB - Académie des sciences, Paris UR - https://numdam.org/articles/10.5802/crmath.424/ DO - 10.5802/crmath.424 LA - en ID - CRMATH_2023__361_G1_437_0 ER -
%0 Journal Article %A Kempf, Volker %T Brezzi–Douglas–Marini interpolation on anisotropic simplices and prisms %J Comptes Rendus. Mathématique %D 2023 %P 437-443 %V 361 %N G1 %I Académie des sciences, Paris %U https://numdam.org/articles/10.5802/crmath.424/ %R 10.5802/crmath.424 %G en %F CRMATH_2023__361_G1_437_0
Kempf, Volker. Brezzi–Douglas–Marini interpolation on anisotropic simplices and prisms. Comptes Rendus. Mathématique, Tome 361 (2023) no. G1, pp. 437-443. doi: 10.5802/crmath.424
[1] Error estimates for Raviart–Thomas interpolation of any order on anisotropic tetrahedra, Math. Comput., Volume 80 (2011) no. 273, pp. 141-163 | MR | Zbl | DOI
[2] Brezzi–Douglas–Marini interpolation of any order on anisotropic triangles and tetrahedra, SIAM J. Numer. Anal., Volume 58 (2020) no. 3, pp. 1696-1718 | MR | Zbl | DOI
[3] Pressure-robust error estimate of optimal order for the Stokes equations: domains with re-entrant edges and anisotropic mesh grading, Calcolo, Volume 58 (2021) no. 2, 15 | MR | Zbl | DOI
[4] Mixed Finite Element Methods and Applications, Springer Series in Computational Mathematics, 44, Springer, 2013 | Zbl | DOI
[5] Anisotropic -norm error estimates for rectangular -elements, Appl. Math. Lett., Volume 121 (2021), 107453 | MR | Zbl | DOI
[6] Pressure-robust discretizations for incompressible flow problems on anisotropic meshes, Doctoral Thesis, Universität der Bundeswehr München, Deutschland (2022)
[7] On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime, Comput. Methods Appl. Mech. Eng., Volume 268 (2014), pp. 782-800 | MR | Zbl | DOI
[8] A new family of mixed finite elements in , Numer. Math., Volume 50 (1986) no. 1, pp. 57-81 | MR | Zbl | DOI
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