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). © 2003 Académie des sciences. Published by Elsevier SAS. All rights reserved.
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