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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 


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).


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).

© 2003  Académie des sciences@@#104156@@

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