Free access
Issue
ESAIM: M2AN
Volume 34, Number 6, November/December 2000
Page(s) 1259 - 1275
DOI http://dx.doi.org/10.1051/m2an:2000126
Published online 15 April 2002
  1. P. Arminjon and M.-C. Viallon, Généralisation du schéma de Nessyahu-Tadmor pour une équation hyperbolique à deux dimensions d'espace. C.R. Acad. Sci. Paris Sér. I 320 (1995) 85-88.
  2. P. Arminjon, M.-C. Viallon and A. Madrane, A finite volume extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for conservation laws on unstructured grids. Int. J. Comput. Fluid Dyn. 9 (1997) 1-22. [CrossRef] [MathSciNet]
  3. F. Bianco, G. Puppo and G. Russo, High order central schemes for hyperbolic systems of conservation laws. SIAM J. Sci. Comput. 21 (1999) 294-322. [CrossRef] [MathSciNet]
  4. B. Einfeldt, On Godunov-type methods for gas dynamics. SIAM J. Numer. Anal. 25 (1988) 294-318. [NASA ADS] [CrossRef] [MathSciNet]
  5. K.O. Friedrichs, Symmetric hyperbolic linear differential equations. Comm. Pure Appl. Math. 7 (1954) 345-392. [CrossRef] [MathSciNet]
  6. A. Harten, The artificial compression method for computation of shocks and contact discontinuities. III. Self-adjusting hybrid schemes. Math. Comp. 32 (1978) 363-389. [MathSciNet]
  7. A. Harten, High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49 (1983) 357-393. [NASA ADS] [CrossRef] [MathSciNet]
  8. A. Harten, B. Engquist, S. Osher and S.R. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes III. J. Comput. Phys. 71 (1987) 231-303. [CrossRef] [MathSciNet]
  9. G.-S. Jiang and E. Tadmor, Non-oscillatory central schemes for multidimensional hyperbolic conservation laws. SIAM J. Sci. Comput. 19 (1998) 1892-1917. [CrossRef] [MathSciNet]
  10. A. Kurganov, Conservation laws: stability of numerical approximations and nonlinear regularization. Ph.D. thesis, Tel-Aviv University, Israel (1997).
  11. A. Kurganov and D. Levy, A third-order semi-discrete central scheme for conservation laws and convection-diffusion equations. SIAM J. Sci. Comput. (to appear).
  12. A. Kurganov and G. Petrova, A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems. Numer. Math. (to appear).
  13. A. Kurganov, S. Noelle and G. Petrova, Semi-Discrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations. SIAM J. Sci. Comput. (submitted).
  14. A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comput. Phys. 160 (2000) 241-282. [NASA ADS] [CrossRef] [MathSciNet]
  15. P.D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 7 (1954) 159-193. [CrossRef] [MathSciNet]
  16. B. van Leer, Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method. J. Comput. Phys. 32 (1979) 101-136. [NASA ADS] [CrossRef]
  17. D. Levy, G. Puppo and G. Russo, Central WENO schemes for hyperbolic systems of conservation laws. ESAIM: M2AN 33 (1999) 547-571. [CrossRef] [EDP Sciences]
  18. D. Levy, G. Puppo and G. Russo, A third order central WENO scheme for 2D conservation laws. Appl. Numer. Math. 33 (2000) 407-414. [CrossRef] [MathSciNet]
  19. D. Levy, G. Puppo and G. Russo, Compact central WENO schemes for multidimensional conservation laws. SIAM J. Sci. Comput. 22 (2000) 656-672. [CrossRef] [MathSciNet]
  20. K.-A. Lie and S. Noelle, Remarks on high-resolution non-oscillatory central schemes for multi-dimensional systems of conservation laws. Part I: An improved quadrature rule for the flux-computation. SIAM J. Sci. Comput. (submitted).
  21. X.-D. Liu and E. Tadmor, Third order nonoscillatory central scheme for hyperbolic conservation laws. Numer. Math. 79 (1998) 397-425. [CrossRef] [MathSciNet]
  22. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408-463. [CrossRef] [MathSciNet]
  23. S. Osher and E. Tadmor, On the convergence of difference approximations to scalar conservation laws. Math. Comp. 50 (1988) 19-51. [CrossRef] [MathSciNet]
  24. R. Sanders and A. Weiser, A high order staggered grid method for hyperbolic systems of conservation laws in one space dimension. Comput. Methods Appl. Mech. Engrg. 75 (1989) 91-107. [CrossRef] [MathSciNet]
  25. R. Sanders and A. Weiser, High resolution staggered mesh approach for nonlinear hyperbolic systems of conservation laws. J. Comput. Phys. 101 (1992) 314-329. [CrossRef] [MathSciNet]
  26. P. Woodward and P. Colella, The numerical solution of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54 (1988) 115-173. [NASA ADS] [CrossRef] [MathSciNet]

Recommended for you