An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations;Un schema «équilibre» et «asymptotic-preserving» pour les equations de la chaleur hyperboliques

Comptes Rendus Mathematique

Volumn 334, Issue 4, 2002, Pages 337-342

  Gosse, Laurent ^a   Toscani, Giuseppe ^a  

^a UNIVERSITY OF PAVIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038392325     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-073X(02)02257-4     Document Type: Article

References (18)

1. D. Amadori, L. Gosse, G. Guerra, Global BV entropy solutions and uniqueness for hyperbolic systems of balance laws, Arch. Rat. Mech. Anal. (to appear). http://www.math.ntnu.no/conservation/2000/050.html.
2. D. Aregba-Driollet, R. Natalini, S.Q. Tang, Diffusive kinetic explicit schemes for nonlinear degenerate parabolic systems, Quaderno IAC 26/2000.
3. M. Arora, Explicit characteristic-based high-resolution algorithms for hyperbolic conservation laws with stiff source terms, Ph.D. thesis, The University of Michigan, 1996, http://hpcc.engin.umich.edu/CFD/users/mohit/html/relaxation.html.
4. F. Bouchut, F.R. Guarguaglini, R. Natalini, Diffusive BGK approximations for nonlinear multidimensional parabolic equations, Indiana Univ. Math. J. 49 (2000) 723-749.
5. C. Cattaneo, Sur une forme de l'équation de la chaleur éliminant le paradoxe d'une propagation instantanée, C. R. Acad. Sci. Paris 247 (1958) 431-433.
6. C. Cercignani, R. Illner, M. Pulvirenti, The Mathematical Theory of Dilute Gases, Appl. Math. Sci., Vol. 106, Springer-Verlag, New York, 1994.
7. E. Gabetta, B. Perthame, Scaling limits for the Ruijgrok-Wu model of the Boltzmann equation, Math. Meth. Appl. Sci. 24 (2001) 949-967.
8. L. Gosse, A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms, Math. Models Methods Appl. Sci. 11 (2001) 339-365.
9. L. Gosse, Localization effects and measure source terms in numerical schemes for balance laws, Math. Comp. posted on November 28, 2001. PII S0025-5718(01)01354-0, to appear in print.
10. J. Greenberg, A.Y. LeRoux, A well balanced scheme for the numerical processing of source terms in hyperbolic equations, SIAM J. Numer. Anal. 33 (1996) 1-16.
11. S. Jin, Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations, SIAM J. Sci. Comput. 21 (1999) 441-454.
12. S. Jin, L. Pareschi, G. Toscani, Diffusive relaxation schemes for multiscale discrete-velocity kinetic equations, SIAM J. Numer. Anal. 35 (1998) 2405-2439.
13. P.G. LeFloch, A.E. Tzavaras, Representation of weak limits and definition of nonconservative products, SIAM J. Math. Anal. 30 (1999) 1309-1342.
14. P.-L. Lions, G. Toscani, Diffusive limit for finite velocity Boltzmann kinetic models, Rev. Mat. Iberoamericana 13 (1997) 473-513.
15. P. Marcati, A. Milani, The one-dimensional Darcy's law as the limit of a compressible Euler flow, J. Differential Equations 84 (1990) 129-147.
16. B. Perthame, C. Simeoni, A kinetic scheme for the Saint-Venant system with a source term, Preprint, 2001.
17. B. Perthame, E. Tadmor, A kinetic equation with kinetic entropy functions for scalar conservation laws, Comm. Math. Phys. 136 (1991) 501-517.
18. T. Platkowski, R. Illner, Discrete velocity models of the Boltzmann equation: a survey on the mathematical aspects of the theory, SIAM Rev. 30 (2) (1988) 213-255.