Sharp CFL, discrete kinetic formulation, and entropic schemes for scalar conservation laws

SIAM Journal on Numerical Analysis

Volumn 41, Issue 3, 2003, Pages 1032-1051

  Makridakis, Charalambos ^a,b   Perthame, Benoît ^c  

^a UNIVERSITY OF CRETE   (Greece)

^b INSTITUTE OF COMPUTER SCIENCE   (Greece)

^c ÉCOLE NORMALE SUPÉRIEURE   (France)

Author keywords

CFL condition; Finite volume methods; Kinetic formulations; Scalar conservation laws

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; ENTROPY; ERROR ANALYSIS; FINITE VOLUME METHOD; KINETIC THEORY; MATHEMATICAL MODELS; VISCOSITY;

FINITE VOLUME METHODS; KINETIC FORMULATIONS; SCALAR CONSERVATION LAWS;

CONSERVATION;

EID: 3142694734     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142902402997     Document Type: Article

References (22)

1. S. BENHARBIT, A. CHALABI, AND J. P. VILA, Numerical viscosity and convergence of finite volume methods for conservation laws with boundary conditions, SIAM J. Numer. Anal., 32 (1995), pp. 775-796.
2. R. BOTCHORISHVILI, B. PERTHAME, AND A. VASSEUR, Equilibrium schemes for scalar conservation laws with stiff sources, Math. Comp., 72 (2003), pp. 131-157.
3. F. BOUCHUT, Construction of BGK models with a family of kinetic entropies for a given system of conservation laws, J. Statist. Phys., 95 (1999), pp. 113-170.
4. Y. BRENIER, Résolution d'équations d'évolution quasilinéaires en dimensions N d'espace à l'aide d'équations linéaires en dimensions N + 1, J. Differential Equations, 50 (1982), pp. 375-390.
5. B. COCKBURN, F. COQUEL, AND P. G. LEFLOCH, An error estimate for finite volume methods for multidimensional conservation laws, Math. Comp., 63 (1994), pp. 77-103.
6. C. M. DAFERMOS, Hyperbolic Conservation Laws in Continuum Physics, Grundlehren Math. Wiss. 325, Springer-Verlag, Berlin, 2000.
7. B. ENQUIST AND S. OSHER, Stable and entropy satisfying approximations for transonic flow calculations, Math. Comp., 31 (1980), pp. 45-75.
8. R. EYMARD, T. GALLOUËT, AND R. HERBIN, Finite Volume Methods, in Handbook of Numerical Analysis, Vol. VII, P. G. Ciarlet and J.-L. Lions, eds., North-Holland, Amsterdam, 2000, pp. 713-1020.
9. E. GODLEWSKI AND P. A. RAVIART, Hyperbolic Systems of Conservation Laws, Ellipses, Paris, 1991.
10. D. KRÓNER, Numerical Schemes for Conservation Laws, Wiley, Chichester, Teubner, Stuttgart, 1997.
11. R. J. LEVEQUE, Numerical Methods for Conservation Laws, Lectures Math. ETH Zurich, Birkhaüser, Basel, 1992.
12. P.-L. LIONS, B. PERTHAME, AND E. TADMOR, Formulation cinétique des lois de conservation scalaires multidimensionnelles, C. R. Acad. Sci. Paris Seŕ. I Math., 312 (1991), pp. 97-102.
13. P.-L. LIONS, B. PERTHAME, AND E. TADMOR, A kinetic formulation of multidimensional scalar conservation, J. Amer. Math. Soc., 7 (1994), pp. 169-191.
14. S. OSHER, Riemann solvers, the entropy condition, and difference approximations, SIAM J. Numer. Anal., 21 (1984), pp. 217-235.
15. S. NOELLE, Convergence of higher order finite volume schemes on irregular grids, Adv. Comput. Math., 3 (1995), pp. 197-218.
16. B. PERTHAME, Kinetic Formulations of Conservation Laws, Oxford University Press, Oxford, UK, 2002.
17. D. SERRE, Systèmes Hyperboliques de Lois de Conservation. I, Diderot, Paris, 1996.
18. D. SERRE, Systèmes Hyperbolique de Lois de Conservation. II, Diderot, Paris, 1996.
19. E. TADMOR, Numerical viscosity and the entropy condition for conservative difference schemes, Math. Comp., 43 (1984), pp. 369-381.
20. A. VASSEUR, Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with γ = 3, Indiana Univ. Math. J., 48 (1999), pp. 347-364.
21. A. VASSEUR, Kinetic semidiscretization of scalar conservation laws and convergence by using averaging lemmas, SIAM J. Numer. Anal., 36 (1999), pp. 465-474.
22. M. WESTDICKENBERG AND S. NOELLE, A new convergence proof for finite volume schemes using the kinetic formulation of conservation laws, SIAM J. Numer. Anal., 37 (2000), pp. 742-757.