An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions
Annales de l'I.H.P. Analyse non linéaire, Volume 21 (2004) no. 5, p. 689-714
@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},
     publisher = {Elsevier},
     volume = {21},
     number = {5},
     year = {2004},
     pages = {689-714},
     doi = {10.1016/j.anihpc.2003.11.001},
     zbl = {1053.35015},
     mrnumber = {2086755},
     language = {en},
     url = {http://www.numdam.org/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, Volume 21 (2004) no. 5, pp. 689-714. doi : 10.1016/j.anihpc.2003.11.001. http://www.numdam.org/item/AIHPC_2004__21_5_689_0/

[1] Bardos C., Le Roux A.Y., Nédélec J.-C., First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations 4 (1979) 1017-1034. | MR 542510 | Zbl 0418.35024

[2] Chainais-Hillairet C., Grenier E., 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] Gisclon M., Serre D., 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] Grenier E., Guès O., Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems, J. Differential Equations 143 (1998) 110-146. | MR 1604888 | Zbl 0896.35078

[5] Guès O., 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] Joseph K.T., Lefloch P.G., Boundary layers in weak solutions of hyperbolic conservation laws, Arch. Ration. Mech. Anal. 147 (1999) 47-88. | MR 1704856 | Zbl 0959.35119

[8] Kružkov S.N., First order quasilinear equations with several independent variables, Mat. Sb. (N.S.) 81 (123) (1970) 228-255. | MR 267257 | Zbl 0215.16203

[9] Kuznecov N.N., 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] Lions P.-L., Perthame B., Tadmor E., 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] Otto F., 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] Perthame B., 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] Tadmor E., Tang T., Pointwise error estimates for relaxation approximations to conservation laws, SIAM J. Math. Anal. 32 (2000) 870-886, (electronic). | MR 1814742 | Zbl 0979.35098

[14] Tang T., 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