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Convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh

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Summary

We study here the discretisation of the nonlinear hyperbolic equationu t +div(vf(u))=0 in ℝ3 × ℝ+, with given initial conditionu(.,0)=u 0(.) in ℝ2, wherev is a function from ℝ2 × ℝ+ to ℝ2 such that divv=0 andf is a given nondecreasing function from ℝ to ℝ. An explicit Euler scheme is used for the time discretisation of the equation, and a triangular mesh for the spatial discretisation. Under a usual stability condition, we prove the convergence of the solution given by an upstream finite volume scheme towards the unique entropy weak solution to the equation.

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Authors and Affiliations

  1. Département Mathématiques, Université de St-Etienne, F-42023, St-Etienne Cedex, France

    S. Champier

  2. Département Mathématiques, Université de Savoie, BP 1104, F-73011, Chambéry Cedex, France

    T. Gallouët & R. Herbin

Authors
  1. S. Champier
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  2. T. Gallouët
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  3. R. Herbin
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Champier, S., Gallouët, T. & Herbin, R. Convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh. Numer. Math. 66, 139–157 (1993). https://doi.org/10.1007/BF01385691

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  • DOI: https://doi.org/10.1007/BF01385691

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