Communications in Mathematical Sciences

Finite volume schemes on Lorentzian manifolds

P. Amorim, P. G. LeFloch, and B. Okutmustur

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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.

Article information

Commun. Math. Sci., Volume 6, Number 4 (2008), 1059-1086.

First available in Project Euclid: 18 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L65: Conservation laws
Secondary: 76L05: Shock waves and blast waves [See also 35L67] 76N

Conservation law Lorenzian manifold entropy condition measure-valued solution finite volume scheme convergence analysis


Amorim, P.; LeFloch, P. G.; Okutmustur, B. Finite volume schemes on Lorentzian manifolds. Commun. Math. Sci. 6 (2008), no. 4, 1059--1086.

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