Finite volume schemes on Lorentzian manifolds

Details Finite volume schemes on Lorentzian manifolds Finite volume schemes on Lorentzian manifolds

2007-12-07

arxiv.org/abs/0712.1221v1

Mathematics

Numerical Analysis

24 pages

Scientific paper

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 accurately and generalize techniques and estimates that were known in the (flat) Euclidian setting, only. The strong convergence of the scheme then is then a consequence of the well-posed theory recently developed by Ben-Artzi and LeFloch for conservation laws on manifolds.

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