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Finite difference schemes for the symmetric Keyfitz–Kranzer system

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Abstract

We are concerned with the convergence of numerical schemes for the initial value problem associated with the Keyfitz–Kranzer system of equations. This system is a toy model for several important models such as in elasticity theory, magnetohydrodynamics, and enhanced oil recovery. In this paper, we prove the convergence of three difference schemes. Two of these schemes are shown to converge to the unique entropy solution. Finally, the convergence is illustrated by several examples.

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Authors and Affiliations

  1. Institut für Mathematik, Julius-Maximilians-Universität Würzburg, Campus Hubland Nord, Emil-Fischer-Strasse 30, 97074, Würzburg, Germany

    Ujjwal Koley

  2. Centre of Mathematics for Applications (CMA), University of Oslo, Blindern, P.O. Box 1053, 0316, Oslo, Norway

    Nils Henrik Risebro

Authors
  1. Ujjwal Koley
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  2. Nils Henrik Risebro
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Correspondence to Ujjwal Koley.

Additional information

This paper was written when NHR was a quest of the Seminar für Angewandte Mathematik, ETH, Zrich. This institution is thanked for its hospitality. UK was supported in part by a Humboldt Research Fellowship through the Alexander von Humboldt Foundation. The anonymous referee is warmly thanked for the thorough reading of the manuscript and for the many useful remarks and suggestions.

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Koley, U., Risebro, N.H. Finite difference schemes for the symmetric Keyfitz–Kranzer system. Z. Angew. Math. Phys. 64, 1057–1085 (2013). https://doi.org/10.1007/s00033-012-0292-y

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  • DOI: https://doi.org/10.1007/s00033-012-0292-y

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