Entropy conditions and their numerical analogues for conservation laws

• Autorzy: R. Ansorge
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1994
• Tom: 29
• Numer: 1
• Strony: 51-63

Daty

wydano

1994

Twórcy

autor

R. Ansorge

• Institute of Applied Mathematics, University of Hamburg, Bundesstr. 55, D-2000 Hamburg 13, Germany

Bibliografia

• [1] R. Courant, K. O. Friedrichs und H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann. 100 (1928), 32-74.
• [2] R. Courant, E. Isaacson and M. Rees, On the solution of nonlinear hyperbolic differential equations by finite differences, Comm. Pure. Appl. Math. 5 (1952), 243-255.
• [3] B. Engquist and S. Osher, Stable and entropy satisfying approximations for transonic flow calculations, Math. Comp. 34 (1980), 45-75.
• [4] A. Harten, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys. 49 (1983), 357-393.
• [5] A. Harten, J. M. Hyman and P. D. Lax, On finite-difference approximations and entropy conditions for shocks, Comm. Pure Appl. Math. 29 (1976), 297-322 (with appendix by Barbara Keyfitz).
• [6] S. N. Kružkov, Generalized solutions of the Cauchy problem in the large for nonlinear equations of first order, Soviet Math. Dokl. 10 (1969), 785-788.
• [7] P. D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math. 7 (1954), 159-193.
• [8] P. D. Lax, Shock waves and entropy, in: Contributions to Nonlinear Functional Analysis, E. Zarantello (ed.), Academic Press, New York 1971, 603-634.
• [9] P. D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves, SIAM Regional Conference Series in Applied Mathematics 11 (1972), 48 pp.
• [10] P. D. Lax and B. Wendroff, Systems of conservation laws, Comm. Pure Appl. Math. 13 (1960), 217-237.
• [11] O. Oleĭnik, Discontinuous solutions of nonlinear differential equations, Amer. Math. Soc. Transl. Ser. 2 26 (1957), 95-172.
• [12] S. Reuter, Die diskrete Entropiebedingung bei der numerischen Lösung skalarer Erhaltungsgleichungen, Diploma Thesis, Hamburg 1991.
• [13] K. G. Strack, Discrete entropy condition and stability for conservation laws, Reports Inst. für Geom. und Prakt. Math., RWTH Aachen 30 (1985).