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Flux-upwind stabilization of the discontinuous Petrov–Galerkin formulation with Lagrange multipliers for advection-diffusion problems

Published online by Cambridge University Press:  15 November 2005

Paola Causin ,
Riccardo Sacco  and
Carlo L. Bottasso
Paola Causin
Affiliation:
INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt BP 105, 78153 Le Chesnay Cedex, France
Riccardo Sacco
Affiliation:
Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, via Bonardi 9, 20133 Milano, Italy. riccardo.sacco@mate.polimi.it
Carlo L. Bottasso
Affiliation:
D. Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, 270 Ferst Dr., 30332 Atlanta GA, USA
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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 H1-norm, and the numerical performance of the scheme is validated on benchmark problems with sharp internal and boundary layers.

Keywords

Finite element methodsmixed and hybrid methodsdiscontinuous Galerkin and Petrov–Galerkin methodsnonconforming finite elementsstabilized finite elementsupwindingadvection-diffusion problems.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 6 , November 2005 , pp. 1087 - 1114
Copyright
© EDP Sciences, SMAI, 2005

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