Analysis of an Asymptotic Preserving Scheme for Relaxation Systems

2011/05/13 by Francis Filbet, Filbet, Francis, Amélie Rambaud +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1105.2655

openalex publication_date 2011/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the convergence of a class of asymptotic preserving numerical schemes initially proposed by F. Filbet & S. Jin \citefilb1 and G. Dimarco & L. Pareschi \citeDimarcoP 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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• Asymptotic preserving schemes for hyperbolic systems with relaxation

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