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

J. Droniou, C. Imbert, J. Vovelle

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

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

Cite this

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An error estimate for the parabolic approximation of multidimentional scalar conservation laws with boundary conditions. / Droniou, J.; Imbert, C.; Vovelle, J.

In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 21, No. 5, 01.01.2004, p. 689-714.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Imbert, C.

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AB - 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.

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KW - Error estimates

KW - Initial-boundary value problem

KW - Kinetic techniques

KW - Parabolic approximation

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JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

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