On a class of implicit and explicit schemes of Van-Leer type for scalar conservation laws
Chalabi, A. ; Vila, J. P.
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 23 (1989), p. 261-282 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1989-01-01
@article{M2AN_1989__23_2_261_0,
     author = {Chalabi, A. and Vila, J. P.},
     title = {On a class of implicit and explicit schemes of Van-Leer type for scalar conservation laws},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {23},
     year = {1989},
     pages = {261-282},
     mrnumber = {1001330},
     zbl = {0667.65075},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1989__23_2_261_0}
}

Chalabi, A.; Vila, J. P. On a class of implicit and explicit schemes of Van-Leer type for scalar conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 23 (1989) pp. 261-282. http://gdmltest.u-ga.fr/item/M2AN_1989__23_2_261_0/

[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. | Zbl 0306.76004

[2] B. Engquist and S. Osher, Stable and entropy condition satisfying approximations for transonic flow calculations, Math. Comp., 34 (1980), pp 45-75. | MR 551290 | Zbl 0438.76051

[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. | MR 731210 | Zbl 0547.65062

[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. | Numdam | MR 618820 | Zbl 0474.65073

[5] A. Majda and S. Osher, Numerical viscosity and the entropy condition, Comm. Pure Appl. Math. 32 (1979), pp 797-834. | MR 539160 | Zbl 0405.76021

[6] M. S. Mock, Some higher order difference schemes enforcing an entropy inequality, Michigan Math. J. 25 (1978), pp. 325-344. | MR 512903 | Zbl 0377.65049

[7] S. Osher and S. Chakravarthy, High resolution schemes and the entropy condition, SIAM J. Number. Anal. 21, 5 (1984), pp. 955-984. | MR 760626 | Zbl 0556.65074

[8] S. Osher, Convergence of generalized MUSCL schemes, SIAM J. Numer. Anal. 22, 5 (1985), pp. 947-961. | MR 799122 | Zbl 0627.35061

[9] B. Van-Leer, Towards the ultimate conservative scheme-5, J. of Comput. Phys. 32, 1 (1979), pp. 101-136. | MR 1703646

[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. | MR 917818 | Zbl 0644.65058

[12] J. P. Vila, P1-methods for the approximation of the conservation laws, To appear in SIAMNUM.