Free access
Volume 39, Number 5, September-October 2005
Page(s) 965 - 993
Published online 15 September 2005
  1. M. Breuß, The correct use of the Lax-Friedrichs method. ESAIM: M2AN 38 (2004) 519–540. [CrossRef] [EDP Sciences]
  2. L. Evans, Partial Differential Equations. American Mathematical Society (1998).
  3. E. Godlewski and P.-A. Raviart, Hyperbolic systems of conservation laws. Edition Marketing (1991).
  4. E. Godlewski and P.-A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer Verlag, New York (1996).
  5. A. Harten, On a class of high order resolution total variation stable finite difference schemes. SIAM J. Numer. Anal. 21 (1984) 1–23. [CrossRef] [MathSciNet]
  6. 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]
  7. G.-S. Jiang, D. Levy, C.T. Lin, S. Osher and E. Tadmor, High-resolution nonoscillatory central schemes with nonstaggered grids for hyperbolic conservation laws. SIAM J. Numer. Anal. 35 (1998) 2147–2168. [CrossRef] [MathSciNet]
  8. S. Jin and Z. Xin, The relaxation scheme for systems of conservation laws in arbitrary space dimension. Comm. Pure Appl. Math. 45 (1995) 235–276. [CrossRef] [MathSciNet]
  9. P.D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical approximation. Comm. Pure Appl. Math. 7 (1954) 159–193. [CrossRef] [MathSciNet]
  10. P.G. Lefloch and J.-G. Liu, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions. Math. Comp. 68 (1999) 1025–1055. [CrossRef] [MathSciNet]
  11. R.J. Leveque, Numerical Methods for Conservation Laws. Birkhäuser Verlag, 2nd Edition (1992).
  12. R.J. Leveque, Finite Volume Methods for Hyperbolic Problems. Cambridge University Press (2002).
  13. 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]
  14. X.D. Liu and E. Tadmor, Third order nonoscillatory central schemes for hyperbolic conservation laws. Numer. Math. 79 (1998) 397–425. [CrossRef] [MathSciNet]
  15. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–436. [CrossRef] [MathSciNet]
  16. E. Tadmor, Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comp. 68 (1984) 1025–1055.
  17. H. Tang and G. Warnecke, A note on (2k + 1)-point conservative monotone schemes. ESAIM: M2AN 38 (2004) 345–358. [CrossRef] [EDP Sciences]

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