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Analysis of an Asymptotic Preserving Scheme for Relaxation Systems∗
Published online by Cambridge University Press: 15 January 2013
Abstract
We consider an asymptotic preserving numerical scheme initially proposed by F. Filbet and S. Jin [J. Comput. Phys. 229 (2010)] and G. Dimarco and L. Pareschi [SIAM J. Numer. Anal. 49 (2011) 2057–2077] 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, vεh) 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.
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 2 , March 2013 , pp. 609 - 633
- Copyright
- © EDP Sciences, SMAI, 2013
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