FINITE VOLUME SCHEMES ON LORENTZIAN MANIFOLDS

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

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6
  • Basım Tarihi: 2008
  • Doi Numarası: 10.4310/cms.2008.v6.n4.a13
  • Dergi Adı: COMMUNICATIONS IN MATHEMATICAL SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1059-1086
  • Anahtar Kelimeler: Conservation law, Lorenzian manifold, entropy condition, measure-valued solution, finite volume scheme, convergence analysis, MULTIDIMENSIONAL CONSERVATION-LAWS, SPACE DIMENSIONS, DIFFERENCE SCHEMES, CONVERGENCE
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

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.