FINITE VOLUME SCHEMES ON LORENTZIAN MANIFOLDS

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Amorim P., Lefloch P. E., Okutmustur B.

COMMUNICATIONS IN MATHEMATICAL SCIENCES, vol.6, pp.1059-1086, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 6
  • Publication Date: 2008
  • Doi Number: 10.4310/cms.2008.v6.n4.a13
  • Journal Name: COMMUNICATIONS IN MATHEMATICAL SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1059-1086
  • Keywords: Conservation law, Lorenzian manifold, entropy condition, measure-valued solution, finite volume scheme, convergence analysis, MULTIDIMENSIONAL CONSERVATION-LAWS, SPACE DIMENSIONS, DIFFERENCE SCHEMES, CONVERGENCE
  • Middle East Technical University Affiliated: No

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.

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.