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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.
Liu et al. (Fri,) studied this question.