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

J. Droniou, C. Imbert, J. Vovelle

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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 η1/3, where η 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.

Original languageEnglish
Pages (from-to)689-714
Number of pages26
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume21
Issue number5
DOIs
Publication statusPublished - 1 Jan 2004
Externally publishedYes

Keywords

  • Conservation law
  • Error estimates
  • Initial-boundary value problem
  • Kinetic techniques
  • Parabolic approximation

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