On the range diminishing property of numerical schemes for scalar conservation laws

Journal of Computational and Applied Mathematics - Tập 381 - Trang 113013 - 2021
A.J. Kriel1
1Department of Mathematics and Applied Mathematics, University of the Free State, PO Box 339, Bloemfontein 9300, South Africa

Tài liệu tham khảo

Harten, 1983, High resolution schemes for hyperbolic conservation laws, J. Comput. Phys., 49, 357, 10.1016/0021-9991(83)90136-5 Laney, 1998 Harten, 1987, Uniformly high-order accurate nonoscillatory schemes I, SIAM J. Numer. Anal., 24, 279, 10.1137/0724022 LeFloch, 1999, Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions, Math. Comput. Amer. Math. Soc., 68, 1025, 10.1090/S0025-5718-99-01062-5 Yang, 1998, On wavewise entropy inequality for high resolution schemes II: Fully discrete MUSCL schemes with exact evolution in small time, SIAM J. Numer. Anal., 36, 1, 10.1137/S0036142995281498 LeVeque, 2002 Sweby, 1984, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal., 21, 995, 10.1137/0721062 Breuß, 2004, The correct use of the Lax-Friedrichs method, ESAIM Math. Model. Numer. Anal., 38, 519, 10.1051/m2an:2004027 Breuss, 2005, An analysis of the influence of data extrema on some first and second order central approximations of hyperbolic conservation laws, ESAIM Math. Model. Numer. Anal., 39, 965, 10.1051/m2an:2005042 Engquist, 1980, Stable and entropy satisfying approximations for transonic flow calculations, Math. Comp., 34, 45, 10.1090/S0025-5718-1980-0551290-1 Nessyahu, 1990, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87, 408, 10.1016/0021-9991(90)90260-8 Tadmor, 1984, Numerical viscosity and the entropy condition for conservative difference schemes, Math. Comp., 43, 369, 10.1090/S0025-5718-1984-0758189-X Li, 2009, Local oscillations in finite difference solutions of hyperbolic conservation laws, Math. Comp., 78, 1997, 10.1090/S0025-5718-09-02219-4