Communications in Mathematical Sciences

Finite volume schemes on Lorentzian manifolds

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

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Abstract

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

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

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.cms/1229619683

Mathematical Reviews number (MathSciNet)
MR2511706

Zentralblatt MATH identifier
1179.35027

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

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

Citation

Amorim, P.; LeFloch, P. G.; Okutmustur, B. Finite volume schemes on Lorentzian manifolds. Commun. Math. Sci. 6 (2008), no. 4, 1059--1086. https://projecteuclid.org/euclid.cms/1229619683


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