Error analysis for a mixed DG method for folded Naghdi's shell

Serge Nicaise; Ismail Merabet

doi:10.1016/j.crma.2015.04.017

Numerical analysis

Error analysis for a mixed DG method for folded Naghdi's shell

Presented by: Olivier Pironneau

Serge Nicaise ¹; Ismail Merabet ²

¹ LAMAV, Université de Valenciennes, France
² LAMA, Université Kasdi Merbah Ouargla, Algeria

Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 659-664.

Abstract
Résumé

In this Note, we perform some error analyses of a mixed discontinuous formulation for Naghdi's equations for thin linearly elastic shells. Using a combination between the a priori and the a posteriori techniques, we derive a quasi-optimal a priori error estimate and an efficient and reliable a posteriori error estimate. Thereby the analysis does not require any additional regularity other than of the weak solution.

Dans cette Note, nous fournissons des estimations d'erreur d'une méthode d'éléments finis discontinus mixte proposée pour résoudre les équations du modèle de Naghdi de coques linéairement élastiques. En utilisant une combinaison entre les techniques de l'analyse a priori et celles de l'analyse a posteriori, nous donnons une estimation d'erreur a priori quasi-optimale et une estimation d'erreur a posteriori fiable et efficace. L'analyse utilisée n'exige aucune regularité additionnelle autre que celle de la solution du problème faible.

Received: 2015-01-23
Accepted: 2015-04-20
Published online: 2015-05-08

DOI: 10.1016/j.crma.2015.04.017

Author's affiliations:

Serge Nicaise ¹; Ismail Merabet ²

¹ LAMAV, Université de Valenciennes, France
² LAMA, Université Kasdi Merbah Ouargla, Algeria

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     author = {Serge Nicaise and Ismail Merabet},
     title = {Error analysis for a mixed {DG} method for folded {Naghdi's} shell},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {659--664},
     publisher = {Elsevier},
     volume = {353},
     number = {7},
     year = {2015},
     doi = {10.1016/j.crma.2015.04.017},
     language = {en},
}

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Serge Nicaise; Ismail Merabet. Error analysis for a mixed DG method for folded Naghdi's shell. Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 659-664. doi : 10.1016/j.crma.2015.04.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.04.017/

References
Cited by

[1] C. Bernardi; A. Blouza; F. Hecht; H. Le Dret A posteriori analysis of finite element discretizations of a Naghdi shell model, IMA J. Numer. Anal., Volume 33 (2013), pp. 190-211

[2] A. Blouza Existence et unicité pour le modèle du Naghdi pour une coque peu régulière, C. R. Acad. Sci. Paris, Ser. I, Volume 324 (1997), pp. 839-844

[3] A. Blouza; H. Le Dret Nagdhi's shell model: existence, uniqueness and continuous dependence on the middle surface, J. Elasticity, Volume 64 (2001), pp. 199-216

[4] A. Blouza; F. Hecht; H. Le Dret Two finite element approximations of Naghdi's shell model in Cartesian coordinates, SIAM J. Numer. Anal., Volume 44 (2006), pp. 636-654

[5] S.C. Brenner; L.R. Scott The Mathematical Theory of Finite Element Methods, Springer-Verlag, New York, 2008

[6] S. Nicaise; I. Merabet A mixed DG method for folded Naghdi's shell in Cartesian coordinates, C. R. Acad. Sci. Paris, Ser. I, Volume 353 (2015)

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