Partial Differential Equations/Numerical Analysis
A non-dissipative entropic scheme for convex scalar equations via discontinuous cell-reconstruction
Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 549-554.

We present a finite volume non-dissipative but entropic scheme for convex scalar equations based on a discontinuous reconstruction of the solution in each cell of the mesh. This discontinuous representation of the numerical solution in each cell is done satisfying the L-norm, Total Variation and entropy decreasing properties. This allows us to prove the convergence towards the unique entropy solution. Numerical computations are reported, showing the non-dissipative behavior of the algorithm.

Nous étudions un schéma de type volumes finis non dissipatif mais entropique pour les équations scalaires à flux convexes. Ce schéma est basé sur une reconstruction de la solution numérique sous forme discontinue à l'intérieur de chaque maille, cette reconstruction étant effectuée en veillant à la décroissance de la norme L, de la variation totale et de l'entropie de la solution discrète. Ceci permet de montrer la convergence de la solution numérique vers l'unique solution entropique. Nous présentons quelques résultats numériques afin de mettre en évidence le caractère non dissipatif de l'algorithme.

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DOI: 10.1016/j.crma.2004.01.024
Lagoutière, Frédéric 1

1 Laboratoire Jacques-Louis-Lions, Université Pierre-et-Marie-Curie, boı̂te courrier 187, 75252 Paris cedex 05, France
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Lagoutière, Frédéric. A non-dissipative entropic scheme for convex scalar equations via discontinuous cell-reconstruction. Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 549-554. doi : 10.1016/j.crma.2004.01.024. http://www.numdam.org/articles/10.1016/j.crma.2004.01.024/

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