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Comptes Rendus Mathématique
Volume 337, n° 12
pages 805-808 (décembre 2003)
Doi : 10.1016/j.crma.2003.10.025
Received : 3 June 2003 ;  accepted : 7 October 2003
Stability of discrete liftings

Víctor  Domínguez a ,  Francisco-Javier  Sayas b
aDep. Matemática e Informática, Univ. Pública de Navarra, Campus de Arrosadía, 31006, Pamplona, Spain 
bDep. Matemática Aplicada, C.P.S., Universidad de Zaragoza, 50018 Zaragoza, Spain 

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In this short Note we prove the equivalence between having a discrete lifting of Dirichlet boundary conditions for (abstract) finite element spaces and having a Scott-Zhang type operator in the space, i.e., a stable projection preserving homogeneous boundary conditions. Both results are equivalent to the possibility of obtaining a Céa estimate where approximation of the boundary conditions is separated from the approximation capabilities of the space. To cite this article: V. Domínguez, F.-J. Sayas, C. R. Acad. Sci. Paris, Ser. I 337 (2003).

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Dans cette courte Note nous démontrons l'équivalence entre l'existence d'un relèvement discret des conditions aux limites de Dirichlet pour un espace (abstrait) d'éléments finis et l'existence d'un opérateur de Scott-Zhang sur l'espace, c'est-à-dire, d'une projection stable qui préserve les conditions aux limites homogènes. Ces deux résultats sont équivalents à la possibilité d'obtenir une estimation de Céa, où l'approximation des conditions aux limites est séparée des propriétés d'approximation de l'espace. Pour citer cet article : V. Domínguez, F.-J. Sayas, C. R. Acad. Sci. Paris, Ser. I 337 (2003).




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