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Annales de l'Institut Henri Poincaré Analyse non linéaire 21, no5 (2004) 689-714

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

Jerome Droniou 1, Cyril Imbert 1, Julien Vovelle 2

(2003)

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.

1:	Institut de Mathématiques et de Modélisation de Montpellier (I3M)
	CNRS : UMR5149 – Université Montpellier II - Sciences et Techniques du Languedoc
2:	Institut de Recherche Mathématique de Rennes (IRMAR)
	CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – INSA Rennes – Université Rennes II

Subject

:

Mathematics/Analysis of PDEs

Keyword(s): conservation law – initial-boundary value problem – error estimates – parabolic approximation – kinetic techniques

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From: Jerome Droniou <>

Submitted on: Wednesday, 8 February 2006 16:03:27

Updated on: Wednesday, 8 February 2006 16:34:56