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.
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.
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Dan Stefanica 1
@article{CRMATH_2004__339_10_739_0, author = {Dan Stefanica}, title = {Lower bounds for additive {Schwarz} methods with mortars}, journal = {Comptes Rendus. Math\'ematique}, pages = {739--743}, publisher = {Elsevier}, volume = {339}, number = {10}, year = {2004}, doi = {10.1016/j.crma.2004.09.016}, language = {en}, }
Dan Stefanica. Lower bounds for additive Schwarz methods with mortars. Comptes Rendus. Mathématique, Volume 339 (2004) no. 10, pp. 739-743. doi : 10.1016/j.crma.2004.09.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.016/
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