Open Access
December 2008 Finite volume schemes on Lorentzian manifolds
P. Amorim, P. G. LeFloch, B. Okutmustur
Commun. Math. Sci. 6(4): 1059-1086 (December 2008).


We investigate the numerical approximation of (discontinuous) entropy solutions to nonlinear hyperbolic conservation laws posed on a Lorentzian manifold. Our main result establishes the convergence of monotone and first-order finite volume schemes for a large class of (space and time) triangulations. The proof relies on a discrete version of entropy inequalities and an entropy dissipation bound, which take into account the manifold geometry and were originally discovered by Cockburn, Coquel, and LeFloch in the (flat) Euclidian setting.


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P. Amorim. P. G. LeFloch. B. Okutmustur. "Finite volume schemes on Lorentzian manifolds." Commun. Math. Sci. 6 (4) 1059 - 1086, December 2008.


Published: December 2008
First available in Project Euclid: 18 December 2008

zbMATH: 1179.35027
MathSciNet: MR2511706

Primary: 35L65
Secondary: 76L05 , 76N

Keywords: conservation law , Convergence analysis , entropy condition , finite volume scheme , Lorenzian manifold , measure-valued solution

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 4 • December 2008
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