Flux-Upwind Stabilization of the Discontinuous Petrov--Galerkin Formulation with Lagrangian Multipliers for Advection-Diffusion Problems

Carlo L. Bottasso Paola Causin 1 Riccardo Sacco
1 BANG - Nonlinear Analysis for Biology and Geophysical flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
Abstract : In this work we consider the dual-primal Discontinuous Petrov-Galerkin (DPG) method for the advection-diffusion model problem. Since in the DPG method both mixed internal variables are discontinuous, a static condensation procedure can be carried out, leading to a single-field nonconforming discretization scheme. For this latter formulation, we propose a flux-upwind stabilization technique to deal with the advection-dominated case. The resulting scheme is conservative and satisfies a discrete maximum principle under standard geometrical assumptions on the computational grid. A convergence analysis is developed, proving first-order accuracy of the method in a discrete H^1-norm, and the numerical performance of the scheme is validated on benchmark problems with sharp internal and boundary layers.
Type de document :
Rapport
[Research Report] RR-5157, INRIA. 2004
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https://hal.inria.fr/inria-00077044
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Soumis le : lundi 29 mai 2006 - 11:58:50
Dernière modification le : vendredi 31 août 2018 - 09:06:03
Document(s) archivé(s) le : lundi 5 avril 2010 - 21:34:31

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Carlo L. Bottasso, Paola Causin, Riccardo Sacco. Flux-Upwind Stabilization of the Discontinuous Petrov--Galerkin Formulation with Lagrangian Multipliers for Advection-Diffusion Problems. [Research Report] RR-5157, INRIA. 2004. 〈inria-00077044〉

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