Comptes Rendus
Partial Differential Equations/Numerical Analysis
Cell centered Galerkin methods
[Méthodes de Galerkine centrées aux mailles]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 31-34.

Dans cette Note, on propose une nouvelle approche pour obtenir et analyser des méthodes d'ordre bas pour les problèmes diffusifs. L'analyse permet d'estimer à la fois le taux de convergence et de prouver la convergence vers des solutions à régularité minimale. Cette approche combine les avancées récentes dans les méthodes de Volumes Finis et de Galerkine discontinues.

In this Note we propose a new approach to obtain and analyze lowest order methods for diffusive problems yielding at the same time convergence rates and convergence to minimal regularity solutions. The approach merges ideas from Finite Volume and discontinuous Galerkin methods.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.11.012

Daniele A. Di Pietro 1

1 Institut français du pétrole, 1 & 4, avenue de Bois Préau, 92852 Rueil Malmaison, France
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     author = {Daniele A. Di Pietro},
     title = {Cell centered {Galerkin} methods},
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     pages = {31--34},
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     doi = {10.1016/j.crma.2009.11.012},
     language = {en},
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Daniele A. Di Pietro. Cell centered Galerkin methods. Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 31-34. doi : 10.1016/j.crma.2009.11.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.11.012/

[1] I. Aavatsmark; G.T. Eigestad; B.T. Mallison; J.M. Nordbotten A compact multipoint flux approximation method with improved robustness, Numer. Methods Partial Differential Equations, Volume 24 (2008) no. 5, pp. 1329-1360

[2] L. Agélas; D.A. Di Pietro; J. Droniou The G method for heterogeneous anisotropic diffusion on general meshes M2AN Math. Model. Numer. Anal. (2009), in press. Preprint available at | HAL

[3] D.N. Arnold; F. Brezzi; B. Cockburn; D. Marini Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal., Volume 39 (2002) no. 5, pp. 1749-1779

[4] D.A. Di Pietro; A. Ern Discrete functional analysis tools for discontinuous Galerkin methods with application to the incompressible Navier–Stokes equations Math. Comp. (2009), in press. Preprint available at | HAL

[5] R. Eymard; T. Gallouët; R. Herbin Discretization of heterogeneous and anisotropic diffusion problems on general non-conforming meshes. SUSHI: a scheme using stabilization and hybrid interfaces IMA J. Num. Anal. (2009), in press. Preprint available at | HAL

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