Analysis of an Asymptotic Preserving Scheme for Relaxation Systems

Abstract. We consider an asymptotic preserving numerical scheme initially proposed by F. Filbet & S. Jin [10] and G. Dimarco & L. Pareschi [9] in the context of nonlinear and stiff kinetic equations. Here, we propose a convergence analysis of such a scheme for the approximation of a system of transport equations with a nonlinear source term, for which the asymptotic limit is given by a conservation law. We investigate the convergence of the approximate solution (uεh, v ε h) to a nonlinear relaxation system, where ε > 0 is a physical parameter and h represents the discretization parameter. Uniform convergence with respect to ε and h is proved and error estimates are also obtained. Finally, several numerical tests are performed to illustrate the accuracy and efficiency of such a scheme.