On a class of implicit and explicit schemes of Van-Leer type for scalar conservation laws
- Volume: 23, Issue: 2, page 261-282
- ISSN: 0764-583X
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top- [1] D. L. BOOK, J. P. BORIS and K. HAIN, Flux-Corrected-Transport II Generalisation of the method, J. of Comp. Phys., 18 (1975), pp 248-283. Zbl0306.76004
- [2] B. ENGQUIST and S. OSHER, Stable and entropy condition satisfying approximations for transonic flow calculations, Math. Comp., 34 (1980), pp 45-75. Zbl0438.76051MR551290
- [3] A. HARTEN, On a class of high resolution total-variation stable finite difference schemes, SIAM J. of Numer. Anal. 21, 1 (1984), pp. 1-23. Zbl0547.65062MR731210
- [4] A. Y. LE ROUX, Convergence of an accurate scheme for first order quasi-linear equations, R.A.I.R.O. Analyse Numérique 15, 2 (1981), pp 151-170. Zbl0474.65073MR618820
- [5] A. MAJDA and S. OSHER, Numerical viscosity and the entropy condition, Comm. Pure Appl. Math. 32 (1979), pp 797-834. Zbl0405.76021MR539160
- [6] M. S. MOCK, Some higher order difference schemes enforcing an entropy inequality, Michigan Math. J. 25 (1978), pp. 325-344. Zbl0377.65049MR512903
- [7] S. OSHER and S. CHAKRAVARTHY, High resolution schemes and the entropy condition, SIAM J. Number. Anal. 21, 5 (1984), pp. 955-984. Zbl0556.65074MR760626
- [8] S. OSHER, Convergence of generalized MUSCL schemes, SIAM J. Numer. Anal. 22, 5 (1985), pp. 947-961. Zbl0627.35061MR799122
- [9] B. VAN-LEER, Towards the ultimate conservative scheme-5, J. of Comput. Phys. 32, 1 (1979), pp. 101-136. MR1703646
- [10] J. P. VILA, Sur la théorie et l'approximation numérique des problèmes hyperboliques non lineaire Applications aux équations de Saint-Venant et a la modélisation des avalanches de neige dense, Thesis, Paris 6 (1986).
- [11] J. P. VILA, High order schemes and entropy condition for nonlinear hyperbolic Systems of conservation laws, Math. of Comp., 50, 181 (1988), 53-73. Zbl0644.65058MR917818
- [12] J. P. VILA, P1-methods for the approximation of the conservation laws, To appear in SIAMNUM.