International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 41510, 15 pages

Error estimates for scalar conservation laws by a kinetic approach

A. Omrane

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.


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.