### 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 | |

Publication status | Published - 1 Jan 2004 |

Externally published | Yes |

### Keywords

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

### Cite this

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*Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire*, vol. 21, no. 5, pp. 689-714. https://doi.org/10.1016/j.anihpc.2003.11.001

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

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - An error estimate for the parabolic approximation of multidimentional scalar conservation laws with boundary conditions

AU - Droniou, J.

AU - Imbert, C.

AU - Vovelle, J.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=4344645755&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2003.11.001

DO - 10.1016/j.anihpc.2003.11.001

M3 - Article

VL - 21

SP - 689

EP - 714

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

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

SN - 0294-1449

IS - 5

ER -