An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions

Abstract : We study the parabolic approximation of a multidimensional scalar conservation law with initial and boundary conditions. We prove that the rate of convergence of the viscous approximation to the weak entropy solution is of order $\\eta^{1/3}$, where $\\eta$ is the size of the artificial viscosity. We use a kinetic formulation and kinetic techniques for initial-boundary value problems developed by the last two authors in a previous work.
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Jerome Droniou, Cyril Imbert, Julien Vovelle. An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2004, 21, no5, pp.689-714. ⟨hal-00018746⟩

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