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| HAL : hal-00432605, version 1 |
| DOI : 10.1007/s00211-011-0430-z |
| Fiche détaillée |  Récupérer au format |
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| Numerische Mathematik (2011) 55 p. |
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| A posteriori error estimates for the effective Hamiltonian of dislocation dynamics |
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| Simone Cacace 1, 2Antonin Chambolle 1 |
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| (2011) |
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| We study an implicit and discontinuous scheme for a non-local Hamilton-Jacobi equation modelling dislocation dynamics. For the evolution problem, we prove an a posteriori estimate of Crandall-Lions type for the error between continuous and discrete solutions. We deduce an a posteriori error estimate for the effective Hamiltonian associated to a stationary cell problem. In dimension one and under suitable assumptions, we also give improved a posteriori estimates. Numerical simulations are provided. |
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| 1 : | Centre de Mathématiques Appliquées (CMAP) |
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CNRS : UMR7641 – Université de Versailles Saint-Quentin-en-Yvelines – Polytechnique - X |
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| 2 : | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| dislocation dynamics – Hamilton-Jacobi – implicit scheme – a posteriori error estimate – effective Hamiltonian – viscosity solutions |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00432605, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00432605 | |
| oai:hal.archives-ouvertes.fr:hal-00432605 | |
| Contributeur : Simone Cacace | |
| Soumis le : Lundi 16 Novembre 2009, 17:35:19 | |
| Dernière modification le : Vendredi 2 Mars 2012, 17:33:39 | |
