Functional analysis/Numerical analysis
A converse to Fortin's Lemma in Banach spaces
Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1092-1095.

We establish the converse of Fortin's Lemma in Banach spaces. This result is useful to assert the existence of a Fortin operator once a discrete inf–sup condition has been proved. The proof uses a specific construction of a right-inverse of a surjective operator in Banach spaces. The key issue is the sharp determination of the stability constants.

On montre une réciproque au lemme de Fortin dans les espaces de Banach. Ce résultat est utile afin d'affirmer l'existence d'un opérateur de Fortin une fois qu'une condition inf–sup discrète a été prouvée. La preuve utilise une construction spécifique d'un inverse à droite d'un opérateur surjectif dans les espaces de Banach. Le point crucial est la détermination précise des constantes de stabilité.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.09.013
Ern, Alexandre 1; Guermond, Jean-Luc 2

1 Université Paris-Est, CERMICS (ENPC), 77455 Marne-la-Vallée cedex 2, France
2 Department of Mathematics, Texas A&M University 3368 TAMU, College Station, TX 77843, USA
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Ern, Alexandre; Guermond, Jean-Luc. A converse to Fortin's Lemma in Banach spaces. Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1092-1095. doi : 10.1016/j.crma.2016.09.013. http://www.numdam.org/articles/10.1016/j.crma.2016.09.013/

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