ArticleOriginal scientific text

Title

Entropy conditions and their numerical analogues for conservation laws

Authors 1

Affiliations

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

Bibliography

  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).
Pages:
51-63
Main language of publication
English
Published
1994
Exact and natural sciences