Communications in Mathematical Sciences
- Commun. Math. Sci.
- Volume 6, Number 4 (2008), 1059-1086.
Finite volume schemes on Lorentzian manifolds
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.
Commun. Math. Sci., Volume 6, Number 4 (2008), 1059-1086.
First available in Project Euclid: 18 December 2008
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35L65: Conservation laws
Secondary: 76L05: Shock waves and blast waves [See also 35L67] 76N
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