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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2013

Analysis of an Asymptotic Preserving Scheme for Relaxation Systems

Francis Filbet
Amélie Rambaud
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Résumé

We study the convergence of a class of asymptotic preserving numerical schemes initially proposed by F. Filbet \& S. Jin \cite{filb1} and G. Dimarco \& L. Pareschi \cite{DimarcoP} in the context of nonlinear and stiff kinetic equations. Here, our analysis is devoted to the approximation of a system of transport equations with a nonlinear source term, for which the asymptotic limit is given by a conservation laws. We investigate the convergence of the approximate solution $(\ueps_h,\veps_h)$ to a nonlinear relaxation system, where $\eps>0$ is a physical parameter and $h$ represents the discretization parameter. Uniform convergence with respect to $\eps$ and $h$ is proven and error estimates are also obtained. Finally, several numerical tests are performed to illustrate the accuracy and efficiency of such a scheme.
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Dates et versions

hal-00592566 , version 1 (13-05-2011)
hal-00592566 , version 2 (13-05-2011)

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Francis Filbet, Amélie Rambaud. Analysis of an Asymptotic Preserving Scheme for Relaxation Systems. ESAIM: Mathematical Modelling and Numerical Analysis, 2013, 47, pp.609-633. ⟨10.1051/m2an/2012042⟩. ⟨hal-00592566v2⟩
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