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| HAL : hal-00364463, version 1 |
| DOI : 10.1051/m2an:2006040 |
| Fiche détaillée |  Récupérer au format |
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| ESAIM: ESAIM: Mathematical Modelling and Numerical Analysis 40, 5 (2006) 923-937 |
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| Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations |
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| Nikolai Yu Bakaev 1Michel Crouzeix 2 |
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| (2006) |
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| In recent years several papers have been devoted to stability and smoothing properties in maximum-norm of finite element discretizations of parabolic problems. Using the theory of analytic semigroups it has been possible to rephrase such properties as bounds for the resolvent of the associated discrete elliptic operator. In all these cases the triangulations of the spatial domain has been assumed to be quasiuniform. In the present paper we show a resolvent estimate, in one and two space dimensions, under weaker conditions on the triangulations than quasiuniformity. In the two-dimensional case, the bound for the resolvent contains a logarithmic factor. |
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| 1 : | Department of Economic Dynamics |
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Moscow Institute of Engineering Physics |
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| 2 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 3 : | Chalmers University of Technology (Chalmers) |
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Chalmers University of Technology |
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| Domaine | : | Mathématiques/Analyse numérique |
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| resolvent estimates – stability – smoothing – maximum – norm – elliptic – parabolic – finite elements – nonquasiuniform triangulations |
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| hal-00364463, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00364463 | |
| oai:hal.archives-ouvertes.fr:hal-00364463 | |
| Contributeur : Dominique Hervé | |
| Soumis le : Jeudi 26 Février 2009, 11:59:27 | |
| Dernière modification le : Jeudi 26 Février 2009, 11:59:27 | |
