Numerical Analysis
External approximation of H 3 (Ω) in a bounded domain of 3 with piecewise cubics of weak C2-class
Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 969-974.

A nonconforming finite element method is introduced to approximate triharmonic boundary value problems in 3 , among other applications. It is constructed upon tetrahedra and piecewise cubic representations. The finite element can be viewed as the primitive of a quadratic one proposed by the first author to solve biharmonic problems, which can be considered in turn as the three-dimensional analogue of the well-known Morley triangle. The new method is proven to be first order convergent in the natural discrete H3-norm for the problem under consideration.

On introduit une méthode d'éléments finis non conformes pour résoudre des problèmes aux limites triharmoniques tridimensionnels, entre autres applications. L'élément fini est basé sur des maillages en tétraèdres et des fonctions cubiques par morceaux. Il est une sorte de primitive d'un autre élément fini quadratique proposé par le premier auteur, pour résoudre des problèmes biharmoniques, ce dernier étant à son tour la version tridimensionnelle du très classique triangle de Morley. On établit pour la nouvelle méthode des résultats de convergence au premier ordre dans la norme H3 discrète, naturelle pour le problème considéré.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.03.038
Ruas, Vitoriano 1; Ghadi, Fattehallah 2; Wakrim, Mohamed 2

1 Laboratoire de modélisation en mécanique, université Paris VI, France
2 Laboratoire d'ingénierie mathématique et d'informatique, faculté des sciences, université Ibn Zohr, Agadir, Morocco
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Ruas, Vitoriano; Ghadi, Fattehallah; Wakrim, Mohamed. External approximation of $ H^{3}\mathrm{(\Omega )}$ in a bounded domain of $ \mathbb{R}^{3}$ with piecewise cubics of weak C2-class. Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 969-974. doi : 10.1016/j.crma.2004.03.038. http://www.numdam.org/articles/10.1016/j.crma.2004.03.038/

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