Uniform stability of a finite difference scheme for transport equations in diffusive regimes

SIAM Journal on Numerical Analysis

Volumn 40, Issue 3, 2002, Pages 891-913

  Klar, A ^a   Unterreiter, A ^b  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Relaxation methods; Stability analysis; Transport equations

Indexed keywords

ITERATIVE METHODS; LINEAR EQUATIONS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES;

TRANSPORT EQUATIONS;

ASYMPTOTIC STABILITY;

EID: 0038042424     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142900375700     Document Type: Article

References (12)

1. R. E. CAFLISCH, S. JIN, AND G. Russo, Uniformly accurate schemes for hyperbolic systems with relaxation, SIAM J. Numer. Anal., 34 (1997), pp. 246-281.
2. F. GOLSE, S. JIN, AND D. LEVERMORE, The convergence of numerical transfer schemes in diffusive regimes 11: The cell edge even parity scheme, in preparation.
3. F. GOLSE, S. JIN, AND C. D. LEVERMORE, The convergence of numerical transfer schemes in diffusive regimes I: Discrete-ordinate method, SIAM J. Numer. Anal., 36 (1999), pp. 1333-1369.
4. S. JIN, Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations, SIAM J. Sci. Comput., 21 (1999), pp. 441-454.
5. S. JIN AND D. LEVERMORE, Fully-discrete numerical transfer in diffusive regimes, Transport Theory Statist. Phys., 22 (1993), pp. 739-791.
6. S. JIN, L. PARESCHI, AND G. TOSCANI, Diffusive relaxation schemes for multiscale discrete-velocity kinetic equations, SIAM J. Numer. Anal., 35 (1998), pp. 2405-2439.
7. S. JIN, L. PARESCHI, AND G. TOSCANI, Uniformly accurate diffusive relaxation schemes for multiscale transport equations. SIAM J. Numer. Anal., 38 (2000), pp. 913-936.
8. A. KLAR, An asymptotic-induced scheme for nonstationary transport equations in the diffusive limit, SIAM J. Numer. Anal., 35 (1998), pp. 1073-1094.
9. A. KLAR, An asymptotic-preserving numerical scheme for kinetic equations in the low mach number limit, SIAM J. Numer. Anal., 36 (1999), pp. 1507-1527.
10. A. KLAR AND C. SCHMEISER, Numerical passage from radiative heat transfer to nonlinear diffusion models, Math. Models Methods Appl. Sci., 11 (2001), pp. 749-767.
11. E. LARSEN, J. MOREL, AND W. MILLER, Asymptotic solution of numerical transport problems in optically thick, diffusive regimes, J. Comput. Phys., 69 (1987), pp. 283-324.
12. C. RINGHOFER, C. SCHMEISER, AND A. ZWIRCHMAYR, Moment methods for the semiconductor Boltzmann equation on bounded position domains, SIAM J. Numer. Anal., 39 (2001), pp. 1078-1095.