@article{AIHPC_2004__21_5_689_0,
author = {Droniou, J. and Imbert, C. and Vovelle, J.},
title = {An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {21},
year = {2004},
pages = {689-714},
doi = {10.1016/j.anihpc.2003.11.001},
mrnumber = {2086755},
zbl = {1053.35015},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_2004__21_5_689_0}
}
Droniou, J.; Imbert, C.; Vovelle, J. An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) pp. 689-714. doi : 10.1016/j.anihpc.2003.11.001. http://gdmltest.u-ga.fr/item/AIHPC_2004__21_5_689_0/
[1] , , , First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations 4 (1979) 1017-1034. | MR 542510 | Zbl 0418.35024
[2] , , Numerical boundary layers for hyperbolic systems in 1-D, M2AN Math. Model. Numer. Anal. 35 (2001) 91-106. | Numdam | MR 1811982 | Zbl 0980.65093
[3] , , Conditions aux limites pour un système strictement hyperbolique fournies par le schéma de Godunov, RAIRO Modél. Math. Anal. Numér. 31 (1997) 359-380. | Numdam | MR 1451347 | Zbl 0873.65087
[4] , , Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems, J. Differential Equations 143 (1998) 110-146. | MR 1604888 | Zbl 0896.35078
[5] , Perturbations visqueuses de problèmes mixtes hyperboliques et couches limites, Ann. Inst. Fourier (Grenoble) 45 (1995) 973-1006. | Numdam | MR 1359836 | Zbl 0831.34023
[6] C. Imbert, J. Vovelle, A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications, SIAM, Mathematical Analysis, in press. | Zbl 1085.35099
[7] , , Boundary layers in weak solutions of hyperbolic conservation laws, Arch. Ration. Mech. Anal. 147 (1999) 47-88. | MR 1704856 | Zbl 0959.35119
[8] , First order quasilinear equations with several independent variables, Mat. Sb. (N.S.) 81 (123) (1970) 228-255. | MR 267257 | Zbl 0215.16203
[9] , The accuracy of certain approximate methods for the computation of weak solutions of a first order quasilinear equation, Ž. Vyčisl. Mat. i Mat. Fiz. 16 (1976) 1489-1502, 1627. | MR 483509 | Zbl 0354.35021
[10] , , , A kinetic formulation of multidimensional scalar conservation laws and related equations, J. Amer. Math. Soc. 7 (1994) 169-191. | MR 1201239 | Zbl 0820.35094
[11] , Initial-boundary value problem for a scalar conservation law, C. R. Acad. Sci. Paris Sér. I Math. 322 (1996) 729-734. | MR 1387428 | Zbl 0852.35013
[12] , Uniqueness and error estimates in first order quasilinear conservation laws via the kinetic entropy defect measure, J. Math. Pures Appl. (9) 77 (1998) 1055-1064. | MR 1661021 | Zbl 0919.35088
[13] , , Pointwise error estimates for relaxation approximations to conservation laws, SIAM J. Math. Anal. 32 (2000) 870-886, (electronic). | MR 1814742 | Zbl 0979.35098
[14] , Error estimates of approximate solutions for nonlinear scalar conservation laws, in: Hyperbolic Problems: Theory, Numerics, Applications (Magdeburg, 2000), vols. I, II, Internat. Ser. Numer. Math., vol. 141, Birkhäuser, Basel, 2001, pp. 873-882. | MR 1871175