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.
Publié le : 2004-07-05
Classification:
conservation law,
initial-boundary value problem,
error estimates,
parabolic approximation,
kinetic techniques,
35L65, 35D99, 35F25, 35F30, 35A35,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00018746,
author = {Droniou, Jerome and Imbert, Cyril and Vovelle, Julien},
title = {An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00018746}
}
Droniou, Jerome; Imbert, Cyril; Vovelle, Julien. An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00018746/