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

J. Droniou; C. Imbert; J. Vovelle

doi:10.1016/j.anihpc.2003.11.001

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 journal › Article › Research › peer-review

7 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 η^1/3, 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 language	English
Pages (from-to)	689-714
Number of pages	26
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	21
Issue number	5
DOIs	https://doi.org/10.1016/j.anihpc.2003.11.001
Publication status	Published - 1 Jan 2004
Externally published	Yes

Keywords

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

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10.1016/j.anihpc.2003.11.001

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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.",

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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.

KW - Conservation law

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

IS - 5

ER -

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

Abstract

Keywords

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