Convergence and error estimates in finite volume schemes for general multidimensional scalar conservation laws. I. Explicite monotone schemes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 28 (1994) no. 3, p. 267-295
@article{M2AN_1994__28_3_267_0,
     author = {Vila, J.-P.},
     title = {Convergence and error estimates in finite volume schemes for general multidimensional scalar conservation laws. I. Explicite monotone schemes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {28},
     number = {3},
     year = {1994},
     pages = {267-295},
     zbl = {0823.65087},
     mrnumber = {1275345},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1994__28_3_267_0}
}
Vila, J.-P. Convergence and error estimates in finite volume schemes for general multidimensional scalar conservation laws. I. Explicite monotone schemes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 28 (1994) no. 3, pp. 267-295. http://www.numdam.org/item/M2AN_1994__28_3_267_0/

[1] S. Benharbit, A. Chalabi, J.-P. Vila, Numerical viscosity, entropy condition and convergence of finite volume scheme for general multidimensional conservation laws, Taormina, 1992. | MR 1262348 | Zbl 0964.65531

[2] S. Benharbit, A. Chalabi, J.-P. Vila, Numerical Viscosity and Convergence of Finite Volume Methods for Conservation Laws with Boundary Conditions, to appear SIAM Journal, on Num. Ana., 1994. | MR 1335655 | Zbl 0865.35082

[3] B. Cockburn, F. Coquel, P. Le Floch, C. W. Shu, Convergence of finite volume methods, Preprint, 1991.

[4] F. Coque, P. Le Floch, Convergence of finite difference schemes for conservation laws in several space dimensions : the corrected antidiffusion flux approach, RI École polytechnique 210, 1990. | MR 1079010 | MR 1046532 | Zbl 0695.65062 | Zbl 0741.35036

[5] S. Champier, T. Gallouet, Convergence d'un schéma décentré amont pour une équation hyperbolique linéaire sur un maillage triangulaire, to appear M2AN. | Numdam | Zbl 0772.65065

[6] S. Champier, T. Gallouet, R. Herbin, Convergence of an upstream finite volume scheme for a non linear hyperbolic equation on a triangular mesh, Preprint, Université de Savoie, 1991. | MR 1245008 | Zbl 0801.65089

[7] M. Crandall, A. Majda, Monotone Difference Approximations for Scalar Conservation Laws, Math. of Comp., 1980, 34, 149, pp. 1-21. | MR 551288 | Zbl 0423.65052

[8] B. Cockburn, On the continuity in BV (Ω) of the L2 projection into finite element spaces, Preprint 90-1, Army High performance comp. res. center Univ. Minnesota. | MR 1094943

[9] M. Crandall, L. Tartar, Some relations beetween nonexpansive and order preserving mappings, Proc. A.M.S., 78, pp. 385-390, 1980. | MR 553381 | Zbl 0449.47059

[10] R. J. Diperna, Measure-valued solution to conservation laws, Arch. Rat. Mech. Anal., 1985, 88, pp. 223-270. | MR 775191 | Zbl 0616.35055

[11] C. Johnson, J. Pitkaranka, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, Math. of Comp., 1984, 47, pp. 285-312. | MR 815828

[12] N. N. Kuznetsov, Accuracy of some approximate methods for computing the weak solution of a first order quasi-linear equation, USSR Comp. Math. and Math. Phys., 1976, 16, pp. 105-119. | MR 483509 | Zbl 0381.35015

[13] N. N. Kuznetsov, S. A. Volosin, On monotone difference approximations for a first order quasilinear equation, Soviet Math. Dokl., 1976, v. 17, pp. 1203-1206. | MR 416050 | Zbl 0361.65082

[14] S. N. Kruzkov, First order quasilinear equations in several independent variables, Math. USSR Sbornik, 1970, 10, pp. 217-243. | MR 267257 | Zbl 0215.16203

[15] P. D. Lax, Shock waves and entropy Contributions to non linear Functional analysis, ed. E. A. Zarantonello, Academic press, 1971. | MR 393870 | MR 367471 | Zbl 0268.35014

[16] S. Osher, Riemann solvers, the entropy condition and difference approximations, Siam. Jour. num. anal., 1984. | MR 736327 | Zbl 0592.65069

[17] A. Szepessi, Convergence of a streamline diffusion finite element method for a conservation law with boundary conditions, RAIRO Model. Math. Anal. Numer., 1991, 25, pp. 749-783. | Numdam | MR 1135992 | Zbl 0751.65061

[18] E. Tadmor, Numerical viscosity and the entropy condition, Math. of Comp., 1984, 43, pp. 369-381. | MR 758189 | Zbl 0587.65058