International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 9, Pages 41510, 15 p.
doi:10.1155/IJMMS/2006/41510
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
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.