# Analysis of an Asymptotic Preserving Scheme for Relaxation Systems

Francis Filbet; Amélie Rambaud

- Volume: 47, Issue: 2, page 609-633
- ISSN: 0764-583X

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topFilbet, Francis, and Rambaud, Amélie. "Analysis of an Asymptotic Preserving Scheme for Relaxation Systems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.2 (2013): 609-633. <http://eudml.org/doc/273321>.

@article{Filbet2013,

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.},

author = {Filbet, Francis, Rambaud, Amélie},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {hyperbolic equations with relaxation; fluid dynamic limit; asymptotic-preserving schemes},

language = {eng},

number = {2},

pages = {609-633},

publisher = {EDP-Sciences},

title = {Analysis of an Asymptotic Preserving Scheme for Relaxation Systems},

url = {http://eudml.org/doc/273321},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Filbet, Francis

AU - Rambaud, Amélie

TI - Analysis of an Asymptotic Preserving Scheme for Relaxation Systems

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 2

SP - 609

EP - 633

AB - 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.

LA - eng

KW - hyperbolic equations with relaxation; fluid dynamic limit; asymptotic-preserving schemes

UR - http://eudml.org/doc/273321

ER -

## References

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