On the conservativity of cell-centered Galerkin methods

Daniele A. Di Pietro

doi:10.1016/j.crma.2013.03.001

Numerical Analysis

On the conservativity of cell-centered Galerkin methods

Presented by: Philippe G. Ciarlet

Daniele A. Di Pietro ¹

¹ University of Montpellier-2, I3M, place Eugène-Bataillon, 34057 Montpellier cedex 5, France

Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 155-159.

Abstract
Résumé

In this work we investigate the conservativity of the cell-centered Galerkin method of Di Pietro (2012) [5] and provide an analytical expression for the conservative flux. The relation with the SUSHI method of Eymard et al. (2010) [10] and with discontinuous Galerkin methods is also explored. The theoretical results are assessed on a numerical example using standard as well as general polygonal grids.

Dans cette note, on étudie la conservativité de la méthode de Galerkine centrée aux mailles de Di Pietro (2012) [5] et on fournit une expression analytique pour le flux numérique. Le lien avec la méthode SUSHI de Eymard et al. (2010) [10] et avec les méthodes de Galerkine discontinues est aussi détaillé. Les résultats théoriques sont validés à la fois sur des maillages standard et polygonaux.

Received: 2013-01-23
Accepted: 2013-03-01
Published online: 2013-02-01

DOI: 10.1016/j.crma.2013.03.001

Author's affiliations:

Daniele A. Di Pietro ¹

¹ University of Montpellier-2, I3M, place Eugène-Bataillon, 34057 Montpellier cedex 5, France

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     author = {Daniele A. Di Pietro},
     title = {On the conservativity of cell-centered {Galerkin} methods},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {155--159},
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     doi = {10.1016/j.crma.2013.03.001},
     language = {en},
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Daniele A. Di Pietro. On the conservativity of cell-centered Galerkin methods. Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 155-159. doi : 10.1016/j.crma.2013.03.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.03.001/

References
Cited by

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[8] D.A. Di Pietro; S. Nicaise A locking-free discontinuous Galerkin method for linear elasticity in locally nearly incompressible heterogeneous media, Appl. Numer. Math., Volume 63 (2013), pp. 105-116

[9] J. Droniou; R. Eymard A mixed finite volume scheme for anisotropic diffusion problems on any grid, Numer. Math., Volume 105 (2006) no. 1, pp. 35-71

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