Finite volume schemes on Lorentzian manifolds
Amorim, P. ; LeFloch, P. G. ; Okutmustur, B.
Commun. Math. Sci., Tome 6 (2008) no. 1, p. 1059-1086 / Harvested from Project Euclid
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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.
Publié le : 2008-12-15
Classification:  Conservation law,  Lorenzian manifold,  entropy condition,  measure-valued solution,  finite volume scheme,  convergence analysis,  35L65,  76L05,  76N 
@article{1229619683,
     author = {Amorim, P. and LeFloch, P. G. and Okutmustur, B.},
     title = {Finite volume schemes on Lorentzian manifolds},
     journal = {Commun. Math. Sci.},
     volume = {6},
     number = {1},
     year = {2008},
     pages = { 1059-1086},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229619683}
}

Amorim, P.; LeFloch, P. G.; Okutmustur, B. Finite volume schemes on Lorentzian manifolds. Commun. Math. Sci., Tome 6 (2008) no. 1, pp.  1059-1086. http://gdmltest.u-ga.fr/item/1229619683/