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Convergence of Path-Conservative Numerical Schemes for Hyperbolic Systems of Balance Laws

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • M. L. Muñoz-Ruiz

    (Universidad de Málaga, Dpt. Análisis Matemático)

  • C. Parés

    (Universidad de Málaga, Dpt. Análisis Matemático)

  • M. J. Castro Díaz

    (Universidad de Málaga, Dpt. Análisis Matemático)

Abstract

We are concerned with the numerical approximation of Cauchy problems for hyperbolic systems of balance laws, which can be studied as a particular case of nonconservative hyperbolic systems. We consider the theory developed by Dal Maso, LeFloch, and Murat to define the weak solutions of nonconservative systems, and path-conservative numerical schemes (introduced by Parés) to numerically approximate these solutions. In a previous work with Le Floch we have studied the appearance of a convergence error measure in the general case of noconservative hyperbolic systems, and we have noticed that this lack of convergence cannot always be observed in numerical experiments. In this work we study the convergence of path-conservative schemes for the special case of systems of balance laws, specifically, the experiments performed up to now show that the numerical solutions converge to the right weak solutions for the correct choice of path-conservative scheme.

Suggested Citation

  • M. L. Muñoz-Ruiz & C. Parés & M. J. Castro Díaz, 2010. "Convergence of Path-Conservative Numerical Schemes for Hyperbolic Systems of Balance Laws," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 675-682, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_72
    DOI: 10.1007/978-3-642-11795-4_72
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