no. G10
Article de recherche - Algorithmes et outils informatiques
The Dual Characteristic-Galerkin Method
[La méthode des caractéristiques-Galerkin duale]
Hecht, Frédéric1 ; Pironneau, Olivier1 
1LJLL, Boite 187, Sorbonne Université, Place Jussieu, 75005 Paris, France
Comptes Rendus. Mathématique, Tome 362 (2024) no. G10, pp. 1109-1119

The Dual Characteristic-Galerkin method (DCGM) is conservative, precise and experimentally positive. We present the method and prove convergence and L 2 -stability in the case of Neumann boundary conditions. In a 2D numerical finite element setting (FEM), the method is compared to Primal Characteristic-Galerkin (PCGM), Streamline upwinding (SUPG), the Dual Discontinuous Galerkin method (DDG) and centered FEM without upwinding. DCGM is difficult to implement numerically but, in the numerical context of this note, it is far superior to all others.

La méthode Dual Characteristic-Galerkin (DCGM) est conservative, précise et expérimentalement positive. Nous prouvons la convergence et la stabilité L 2 . Dans le cadre numérique des méthodes d’éléments finis (FEM) en 2D, la méthode est comparée à la méthode Primal Characteristic-Galerkin (PCGM), au Streamline upwinding (SUPG), à la méthode Dual Discontinuous Galerkin (DDG) et à une discretisation FEM sans décentrage. La méthode DCGM est difficile à mettre en œuvre numériquement, mais elle est de loin supérieure à toutes les autres dans le cadre étudié dans cette note.

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Accepté le :
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DOI : 10.5802/crmath.598
Classification : 35Q35, 65M06, 65M15, 65M25, 65M60
Keywords: Partial differential equations, convection-diffusion, numerical method, finite element method
Mots-clés : Équations aux dérivées partielles, convection-diffusion, schémas numériques, éléments finis

Hecht, Frédéric  1   ; Pironneau, Olivier  1

1 LJLL, Boite 187, Sorbonne Université, Place Jussieu, 75005 Paris, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Hecht, Frédéric; Pironneau, Olivier. The Dual Characteristic-Galerkin Method. Comptes Rendus. Mathématique, Tome 362 (2024) no. G10, pp. 1109-1119. doi: 10.5802/crmath.598

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