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Comptes Rendus Mathématique
Volume 339, n° 10
pages 739-743 (novembre 2004)
Doi : 10.1016/j.crma.2004.09.016
Received : 3 Mars 2004 ;  accepted : 3 September 2004
Lower bounds for additive Schwarz methods with mortars
Bornes inférieures pour méthode de Schwarz additives et éléments finis avec joints.
 

Dan Stefanica
Baruch College, City University of New York, One Bernard Baruch Way, Box B 6-230, New York, NY 10010, USA 

Abstract

We establish lower bounds for the condition number of overlapping additive Schwarz algorithms for elliptic problems discretized by mortar finite elements. These bounds coincide, up to constants, with the classical upper bounds from the literature. The optimality of the condition number estimates is thus established. To cite this article: D. Stefanica, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.
Résumé

On détermine des bornes inférieures de conditionnement d'algorithmes de type Schwarz additif pour des problèmes elliptiques discrétisés par éléments finis avec joints. Ces limites sont identiques à des constantes multiplicatives près, aux bornes supérieures classiques établies par ailleurs. L'optimalité du conditionnement est ainsi démontré. Pour citer cet article : D. Stefanica, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.


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