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.
Domínguez, V., & Sayas, F. J. (2003). Stability of discrete liftings. Comptes Rendus Mathematique, 337(12), 805–808. https://doi.org/10.1016/j.crma.2003.10.025