Comptes Rendus
no. 13-14
Numerical Analysis
Entropy-based nonlinear viscosity for Fourier approximations of conservation laws
[Une technique de viscosité entropique pour l'approximation de Fourier des lois de conservation]

Présenté par : Olivier Pironneau

Jean-Luc Guermond1 ; Richard Pasquetti2
1 Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
2 Laboratoire J.A. Dieudonné, UMR CNRS 6621, Université de Nice-Sophia Antipolis, parc Valrose, 06108 Nice cedex 02, France
Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 801-806.

On propose une technique de viscosité non-linéaire entropique pour approcher les lois de conservation par une méthode spectrale Fourier. La viscosité est proportionelle au résidu de l'équation d'évolution de l'entropie et est ainsi spectralement petite quand la solution est régulière.

An Entropy-based nonlinear viscosity for approximating conservation laws using Fourier expansions is proposed. The viscosity is proportional to the entropy residual of the equation (or system) and thus preserves the spectral accuracy of the method.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.05.013
Jean-Luc Guermond 1 ; Richard Pasquetti 2

1 Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
2 Laboratoire J.A. Dieudonné, UMR CNRS 6621, Université de Nice-Sophia Antipolis, parc Valrose, 06108 Nice cedex 02, France 
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     title = {Entropy-based nonlinear viscosity for {Fourier} approximations of conservation laws},
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Jean-Luc Guermond; Richard Pasquetti. Entropy-based nonlinear viscosity for Fourier approximations of conservation laws. Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 801-806. doi : 10.1016/j.crma.2008.05.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.05.013/

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