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Numerische Mathematik

, Volume 89, Issue 3, pp 493–509 | Cite as

A fully discrete scheme for diffusive-dispersive conservation laws

  • C. Chalons
  • P.G. LeFloch
Original article

Summary.

We introduce a fully discrete (in both space and time) scheme for the numerical approximation of diffusive-dispersive hyperbolic conservation laws in one-space dimension. This scheme extends an approach by LeFloch and Rohde [4]: it satisfies a cell entropy inequality and, as a consequence, the space integral of the entropy is a decreasing function of time. This is an important stability property, shared by the continuous model as well. Following Hayes and LeFloch [2], we show that the limiting solutions generated by the scheme need not coincide with the classical Oleinik-Kruzkov entropy solutions, but contain nonclassical undercompressive shock waves. Investigating the properties of the scheme, we stress various similarities and differences between the continuous model and the discrete scheme (dynamics of nonclassical shocks, nucleation, etc).

Mathematics Subject Classification (2000): 65M06, 35L65 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • C. Chalons
    • 1
  • P.G. LeFloch
    • 1
  1. 1.Centre de Mathématiques Appliquées & Centre National de la Recherche Scientifique, U.M.R. 7641, Ecole Polytechnique, 91128 Palaiseau Cedex, France; e-mail: lefloch@cmap.polytechnique.fr. FR

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