Comptes Rendus
Numerical analysis
Brezzi–Douglas–Marini interpolation on anisotropic simplices and prisms
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 437-443.

The Brezzi–Douglas–Marini interpolation error on anisotropic elements has been analyzed in two recent publications, the first focusing on simplices with estimates in L 2 , the other considering parallelotopes with estimates in terms of L p -norms. This contribution provides generalized estimates for anisotropic simplices for the L p case, 1p, 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 2 , l’autre considérant les parallelotopes avec des estimations en termes de normes L p . Notre contribution fournit des estimations généralisées pour les simplexes anisotropes pour le cas L p , 1p, et montre de nouvelles estimations pour les prismes anisotropes à base triangulaire.

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DOI: 10.5802/crmath.424
Classification: 65D05, 65N30

Volker Kempf 1

1 Universität der Bundeswehr München, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Volker Kempf. Brezzi–Douglas–Marini interpolation on anisotropic simplices and prisms. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 437-443. doi : 10.5802/crmath.424. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.424/

[1] Gabriel Acosta; Thomas Apel; Ricardo G. Durán; Ariel L. Lombardi Error estimates for Raviart–Thomas interpolation of any order on anisotropic tetrahedra, Math. Comput., Volume 80 (2011) no. 273, pp. 141-163 | DOI | MR | Zbl

[2] Thomas Apel; Volker Kempf Brezzi–Douglas–Marini interpolation of any order on anisotropic triangles and tetrahedra, SIAM J. Numer. Anal., Volume 58 (2020) no. 3, pp. 1696-1718 | DOI | MR | Zbl

[3] Thomas Apel; Volker Kempf 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 | DOI | MR | Zbl

[4] Daniele Boffi; Franco Brezzi; Michel Fortin Mixed Finite Element Methods and Applications, Springer Series in Computational Mathematics, 44, Springer, 2013 | DOI | Zbl

[5] Sebastian Franz Anisotropic H div -norm error estimates for rectangular H div -elements, Appl. Math. Lett., Volume 121 (2021), 107453 | DOI | MR | Zbl

[6] Volker Kempf Pressure-robust discretizations for incompressible flow problems on anisotropic meshes, Doctoral Thesis, Universität der Bundeswehr München, Deutschland (2022)

[7] Alexander Linke 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 | DOI | MR | Zbl

[8] Jean-Claude Nédélec A new family of mixed finite elements in 3 , Numer. Math., Volume 50 (1986) no. 1, pp. 57-81 | DOI | MR | Zbl

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