ABGRALL, Remi; KRUST, Arnaud

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ABGRALL, Remi
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]

KRUST, Arnaud
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]

Langue

Rapport

Ce document a été publié dans

2012-01p. 24

Résumé en anglais

We are interested in developing a numerical framework well suited for advection-diffusion problems when the advection part is dominant. In that case, given Dirichlet type boundary condition, it is well known that a boundary layer develops. In order to resolve correctly this layer, standard methods consist in increasing the mesh resolution and possibly increasing the formal accuracy of the numerical method. In this paper, we follow another path: we do not seek to increase the formal accuracy of the scheme but, by a careful choice of finite element, to lower the mesh resolution in the layer. Indeed the finite element representation we choose is locally the sum of a standard one plus an enrichment. This paper proposes such a method and with several numerical examples, we show the potential of this approach. In particular we show that the method is not very sensitive to the choice of the enrichment.< Réduire

Mots clés en anglais

enrichment

adaptivity

stabilized finite elements

XFEM

boundary-layer

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189888

Projet Européen

Adaptive Schemes for Deterministic and Stochastic Flow Problems

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251