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| HAL : hal-00193540, version 3 |
| DOI : 10.1016/j.cam.2009.12.009 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Computational and Applied Mathematics 234, 1 (2009) 114-130 |
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| Versions disponibles : | v1 (04-12-2007) | v2 (06-08-2008) | v3 (08-11-2008) |
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| Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems |
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| Alexandre Ern 1Annette Stephansen 1, 2 |
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| (16/12/2009) |
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| We propose and study a posteriori error estimates for convection-diffusion-reaction problems with inhomogeneous and anisotropic diffusion approximated by weighted interior-penalty discontinuous Galerkin methods. Our twofold objective is to derive estimates without undetermined constants and to analyze carefully the robustness of the estimates in singularly perturbed regimes due to dominant convection or reaction. We first derive locally computable estimates for the error measured in the energy (semi)norm. These estimates are evaluated using H(div)-conforming diffusive and convective flux reconstructions, thereby extending previous work on pure diffusion problems. The resulting estimates are semi-robust in the sense that local lower error bounds can be derived using suitable cutoff functions of the local Peclet and Damkohler numbers. Fully robust estimates are obtained for the error measured in an augmented norm consisting of the energy (semi)norm, a dual norm of the skew-symmetric part of the differential operator, and a suitable contribution of the interelement jumps of the discrete solution. Numerical experiments are presented to illustrate the theoretical results. |
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| 1 : | 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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| 2 : | Agence Nationale pour la Gestion des Déchets Radioactifs (ANDRA) |
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ANDRA |
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| 3 : | Laboratoire Jacques-Louis Lions (LJLL) |
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CNRS : UMR7598 – Université Paris VI - Pierre et Marie Curie |
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| Domaine | : | Mathématiques/Analyse numérique |
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| convection--diffusion--reaction – discontinuous Galerkin methods – a posteriori error estimates – dominant convection – dominant reaction – robustness |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00193540, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00193540 | |
| oai:hal.archives-ouvertes.fr:hal-00193540 | |
| Contributeur : Martin Vohralík | |
| Soumis le : Vendredi 7 Novembre 2008, 23:03:16 | |
| Dernière modification le : Dimanche 9 Mai 2010, 13:58:58 | |
