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Convergence of flux vector splitting schemes with single entropy inequality for hyperbolic systems of conservation laws

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Summary.

We prove the convergence of flux vector splitting schemes associated to hyperbolic systems of conservation laws with a single compatible entropy η c . We prove estimate on the L2 norm of the gradient of the numerical approximation in the inverse square root of the space increment Δx. This estimate is related to the notion of (strictly) η c -dissipativity on F+, −F− and Id−λ(F+−F−), where F+, F− is the flux-decomposition. The second tool of the proof is a kinetic formulation of the flux-splitting scheme with three velocities. Then we get a control for all entropies and apply the compensated compactness theory.

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Authors and Affiliations

  1. Laboratoire J. A. Dieudonné, UMR CNRS 6621, Université de Nice Sophia-Antipolis, Parc Valrose, 06108, Nice cedex 2, France

    F. Berthelin

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  1. F. Berthelin
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Correspondence to F. Berthelin.

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Mathematics Subject Classification (2000): 65M12, 35L65, 65M06, 82C40

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Berthelin, F. Convergence of flux vector splitting schemes with single entropy inequality for hyperbolic systems of conservation laws. Numer. Math. 99, 585–604 (2005). https://doi.org/10.1007/s00211-004-0567-0

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  • DOI: https://doi.org/10.1007/s00211-004-0567-0

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