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.

Flux-Upwind Stabilization of the Discontinuous Petrov-Galerkin Formulation with Lagrangian Multipliers for Advection-Diffusion Problems / P.Causin, R. Sacco, C. Bottasso. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - 39:6(2005), pp. 1087-1114.

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

P.Causin
Primo
;
2005

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.
Advection-diffusion problems; Discontinuous Galerkin and Petrov-Galerkin methods; Finite element methods; Mixed and hybrid methods; Nonconforming finite elements; Stabilized finite elements; Upwinding
Settore MAT/08 - Analisi Numerica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/17367
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