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Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

Jian-Guo Liu Duke University Luc Mieussens Universit´e de Bordeaux

Numerical Analysis and Scientific Computing mathscidoc:1702.25033

SIAM Journal on Numerical Analysis , 48, (4), 2010.8
We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31, pp. 334-368, 2008] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths, and is close to a convection CFL condition for large mean free paths. Ou r analysis is based on very simple energy estimates.
transport equations, diffusion limit, asymptotic preserving schemes, stiff terms, stability analysis
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@inproceedings{jian-guo2010analysis,
  title={Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit},
  author={Jian-Guo Liu, and Luc Mieussens},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209000110110672345},
  booktitle={SIAM Journal on Numerical Analysis },
  volume={48},
  number={4},
  year={2010},
}
Jian-Guo Liu, and Luc Mieussens. Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit. 2010. Vol. 48. In SIAM Journal on Numerical Analysis . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209000110110672345.
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