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| HAL : hal-00454133, version 3 |
| arXiv : 1002.1772 |
| DOI : 10.1142/S0218202512500157 |
| Fiche détaillée |  Récupérer au format |
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| Mathematical Models and Methods in Applied Sciences 22, 8 (2012) 63 pages |
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| Versions disponibles : | v1 (09-02-2010) | v2 (29-10-2010) | v3 (28-10-2011) |
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| Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra |
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| Martin Costabel 1Monique Dauge 1 |
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| (2012) |
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| We prove weighted anisotropic analytic estimates for solutions of second order elliptic boundary value problems in polyhedra. The weighted analytic classes which we use are the same as those introduced by Guo in 1993 in view of establishing exponential convergence for hp finite element methods in polyhedra. We first give a simple proof of the known weighted analytic regularity in a polygon, relying on a new formulation of elliptic a priori estimates in smooth domains with analytic control of derivatives. The technique is based on dyadic partitions near the corners. This technique can successfully be extended to polyhedra, providing isotropic analytic regularity. This is not optimal, because it does not take advantage of the full regularity along the edges. We combine it with a nested open set technique to obtain the desired three-dimensional anisotropic analytic regularity result. Our proofs are global and do not require the analysis of singular functions. |
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| 1 : | 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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| 2 : | Laboratoire de Mathématiques et leurs Applications de Valenciennes, EA 45 (LAMAV) |
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Université de Valenciennes et du Hainaut-Cambresis – CNRS : FRE2956 |
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| Analyse numérique |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles Mathématiques/Analyse numérique |
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| Weighted anisotropic Sobolev spaces – regularity estimates |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00454133, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00454133 | |
| oai:hal.archives-ouvertes.fr:hal-00454133 | |
| Contributeur : Monique Dauge | |
| Soumis le : Vendredi 28 Octobre 2011, 08:15:32 | |
| Dernière modification le : Jeudi 6 Septembre 2012, 15:43:38 | |
