Flux-Upwind Stabilization of the Discontinuous Petrov--Galerkin Formulation with Lagrangian Multipliers for Advection-Diffusion Problems - Laboratoire Jacques-Louis Lions Accéder directement au contenu
Rapport (Rapport De Recherche) Année : 2004

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

Résumé

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.
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Dates et versions

inria-00077044 , version 1 (29-05-2006)

Identifiants

  • HAL Id : inria-00077044 , version 1

Citer

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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