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

Publication
, Journal Article

Liu, JG; Mieussens, L

Published in: SIAM J. Numer. Anal.

2010

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334–368] 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. Our analysis is based on very simple energy estimates.

### Duke Scholars

## Published In

SIAM J. Numer. Anal.

## Publication Date

2010

## Volume

48

## Start / End Page

1474 / 1491

## Related Subject Headings

- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

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MLA

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Liu, J. G., & Mieussens, L. (2010). Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit.

*SIAM J. Numer. Anal.*,*48*, 1474–1491.Liu, J. G., and L. Mieussens. “Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit.”

*SIAM J. Numer. Anal.*48 (2010): 1474–91.Liu JG, Mieussens L. Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit. SIAM J Numer Anal. 2010;48:1474–91.

Liu, J. G., and L. Mieussens. “Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit.”

*SIAM J. Numer. Anal.*, vol. 48, 2010, pp. 1474–91.Liu JG, Mieussens L. Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit. SIAM J Numer Anal. 2010;48:1474–1491.

## Published In

SIAM J. Numer. Anal.

## Publication Date

2010

## Volume

48

## Start / End Page

1474 / 1491

## Related Subject Headings

- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics