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Analysis of an Asymptotic Preserving Scheme for Relaxation Systems∗

Published online by Cambridge University Press:  15 January 2013

Francis Filbet  and
Amélie Rambaud
Francis Filbet
Affiliation:
Université de Lyon, UMR5208, Institut Camille Jordan, Université Claude Bernard Lyon 1 43 boulevard 11 novembre 1918, 69622 Villeurbanne Cedex, France.. filbet@math.univ-lyon1.fr; rambaud@math.univ-lyon1.fr
Amélie Rambaud
Affiliation:
Université de Lyon, UMR5208, Institut Camille Jordan, Université Claude Bernard Lyon 1 43 boulevard 11 novembre 1918, 69622 Villeurbanne Cedex, France.. filbet@math.univ-lyon1.fr; rambaud@math.univ-lyon1.fr
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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.

Keywords

Hyperbolic equations with relaxationfluid dynamic limitasymptotic-preserving schemes
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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References

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