- M. Breuß, The correct use of the Lax-Friedrichs method. ESAIM: M2AN 38 (2004) 519–540. [CrossRef] [EDP Sciences]
- L. Evans, Partial Differential Equations. American Mathematical Society (1998).
- E. Godlewski and P.-A. Raviart, Hyperbolic systems of conservation laws. Edition Marketing (1991).
- E. Godlewski and P.-A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer Verlag, New York (1996).
- 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]
- 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]
- 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]
- 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]
- P.D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical approximation. Comm. Pure Appl. Math. 7 (1954) 159–193. [CrossRef] [MathSciNet]
- 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]
- R.J. Leveque, Numerical Methods for Conservation Laws. Birkhäuser Verlag, 2nd Edition (1992).
- R.J. Leveque, Finite Volume Methods for Hyperbolic Problems. Cambridge University Press (2002).
- 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]
- X.D. Liu and E. Tadmor, Third order nonoscillatory central schemes for hyperbolic conservation laws. Numer. Math. 79 (1998) 397–425. [CrossRef] [MathSciNet]
- H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–436. [CrossRef] [MathSciNet]
- E. Tadmor, Numerical viscosity and the entropy condition for conservative difference schemes. Math. Comp. 68 (1984) 1025–1055.
- H. Tang and G. Warnecke, A note on (2k + 1)-point conservative monotone schemes. ESAIM: M2AN 38 (2004) 345–358. [CrossRef] [EDP Sciences]
Volume 39, Number 5, September-October 2005
|Page(s)||965 - 993|
|Published online||15 September 2005|