Entropy conditions and their numerical analogues for conservation laws

R. Ansorge

Banach Center Publications (1994)

  • Volume: 29, Issue: 1, page 51-63
  • ISSN: 0137-6934

How to cite

top

Ansorge, R.. "Entropy conditions and their numerical analogues for conservation laws." Banach Center Publications 29.1 (1994): 51-63. <http://eudml.org/doc/262601>.

@article{Ansorge1994,
author = {Ansorge, R.},
journal = {Banach Center Publications},
keywords = {entropy conditions; conservation laws; flow problems; weak solutions; consistency; difference method; Lax-Wendroff method; monotone method; total variance diminishing method; TVD method},
language = {eng},
number = {1},
pages = {51-63},
title = {Entropy conditions and their numerical analogues for conservation laws},
url = {http://eudml.org/doc/262601},
volume = {29},
year = {1994},
}

TY - JOUR
AU - Ansorge, R.
TI - Entropy conditions and their numerical analogues for conservation laws
JO - Banach Center Publications
PY - 1994
VL - 29
IS - 1
SP - 51
EP - 63
LA - eng
KW - entropy conditions; conservation laws; flow problems; weak solutions; consistency; difference method; Lax-Wendroff method; monotone method; total variance diminishing method; TVD method
UR - http://eudml.org/doc/262601
ER -

References

top
  1. [1] R. Courant, K. O. Friedrichs und H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann. 100 (1928), 32-74. Zbl54.0486.01
  2. [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. Zbl0047.11704
  3. [3] B. Engquist and S. Osher, Stable and entropy satisfying approximations for transonic flow calculations, Math. Comp. 34 (1980), 45-75. Zbl0438.76051
  4. [4] A. Harten, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys. 49 (1983), 357-393. Zbl0565.65050
  5. [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). Zbl0351.76070
  6. [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. [7] P. D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math. 7 (1954), 159-193. Zbl0055.19404
  8. [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. [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. [10] P. D. Lax and B. Wendroff, Systems of conservation laws, Comm. Pure Appl. Math. 13 (1960), 217-237. Zbl0152.44802
  11. [11] O. Oleĭnik, Discontinuous solutions of nonlinear differential equations, Amer. Math. Soc. Transl. Ser. 2 26 (1957), 95-172. 
  12. [12] S. Reuter, Die diskrete Entropiebedingung bei der numerischen Lösung skalarer Erhaltungsgleichungen, Diploma Thesis, Hamburg 1991. 
  13. [13] K. G. Strack, Discrete entropy condition and stability for conservation laws, Reports Inst. für Geom. und Prakt. Math., RWTH Aachen 30 (1985). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.