International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 41510, 15 pages
doi:10.1155/IJMMS/2006/41510
Error estimates for scalar conservation laws by a kinetic approach
Département de Mathématiques et Informatique, Université des Antilles et de la Guyane, Campus de Fouillole, Pointe à Pitre Cedex, Guadeloupe 97159, France
Received 13 March 2006; Accepted 13 April 2006
Copyright © 2006 A. Omrane. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We use the kinetic approach of Perthame and Tadmor
(1991) to calculate the error estimates for general
scalar conservation laws governing problems in gas dynamics or
fluid mechanics in general. The Kružkov and Kuznetsov
techniques are generalized to this method, and an error bound of
order ε (where ε is the mean free path) is obtained.