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Convergence of the Upwind Interface Source Method for Hyperbolic Conservation Laws

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

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  • Benoît Perthame

    (École Normale Supérieure, Département de Mathématiques et Applications)

  • Chiara Simeoni

    (École Normale Supérieure, Département de Mathématiques et Applications)

Abstract

This paper deals with typical questions arising in the analysis of numerical approximations for scalar conservation laws with a source term. We focus our attention on semi-discrete finite volume schemes, in the general case of a nonuniform spatial mesh. To define appropriate discretizations of the source term, we introduce the formalism peculiar to the Upwind Interface Source method and we establish conditions on the numerical functions so that the discrete solver preserves the steady state solutions. Then we formulate a rigorous definition of consistency, adapted to the class of well-balanced schemes, for which we are able to prove a Lax-Wendroff type convergence theorem. Some examples of numerical methods are discussed, in order to validate the arguments we propose.

Suggested Citation

  • Benoît Perthame & Chiara Simeoni, 2003. "Convergence of the Upwind Interface Source Method for Hyperbolic Conservation Laws," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 61-78, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_5
    DOI: 10.1007/978-3-642-55711-8_5
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