Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes
Journal of Computational Physics
An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit
SIAM Journal on Numerical Analysis
Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations
SIAM Journal on Numerical Analysis
A Numerical Method for Kinetic Semiconductor Equations in the Drift-Diffusion Limit
SIAM Journal on Scientific Computing
An Asymptotic Preserving Numerical Scheme for Kinetic Equations in the Low Mach Number Limit
SIAM Journal on Numerical Analysis
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
SIAM Journal on Scientific Computing
Discretization of the multiscale semiconductor Boltzmann equation by diffusive relaxation schemes
Journal of Computational Physics
Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
SIAM Journal on Numerical Analysis
Uniform Stability of a Finite Difference Scheme for Transport Equations in Diffusive Regimes
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Numerical Schemes of Diffusion Asymptotics and Moment Closures for Kinetic Equations
Journal of Scientific Computing
SIAM Journal on Scientific Computing
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II
Journal of Computational Physics
Computers & Mathematics with Applications
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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.