An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions

J. Droniou; C. Imbert; J. Vovelle

Annales de l'I.H.P. Analyse non linéaire (2004)

  • Volume: 21, Issue: 5, page 689-714
  • ISSN: 0294-1449

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Droniou, J., Imbert, C., and 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 21.5 (2004): 689-714. <http://eudml.org/doc/78635>.

@article{Droniou2004,
author = {Droniou, J., Imbert, C., Vovelle, J.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {initial-boundary value problem; kinetic techniques},
language = {eng},
number = {5},
pages = {689-714},
publisher = {Elsevier},
title = {An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions},
url = {http://eudml.org/doc/78635},
volume = {21},
year = {2004},
}

TY - JOUR
AU - Droniou, J.
AU - Imbert, C.
AU - Vovelle, J.
TI - An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2004
PB - Elsevier
VL - 21
IS - 5
SP - 689
EP - 714
LA - eng
KW - initial-boundary value problem; kinetic techniques
UR - http://eudml.org/doc/78635
ER -

References

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  1. [1] Bardos C., le Roux A.Y., Nédélec J.-C., First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations4 (1979) 1017-1034. Zbl0418.35024MR542510
  2. [2] Chainais-Hillairet C., Grenier E., Numerical boundary layers for hyperbolic systems in 1-D, M2AN Math. Model. Numer. Anal.35 (2001) 91-106. Zbl0980.65093MR1811982
  3. [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. Zbl0873.65087MR1451347
  4. [4] Grenier E., Guès O., Boundary layers for viscous perturbations of noncharacteristic quasilinear hyperbolic problems, J. Differential Equations143 (1998) 110-146. Zbl0896.35078MR1604888
  5. [5] Guès O., Perturbations visqueuses de problèmes mixtes hyperboliques et couches limites, Ann. Inst. Fourier (Grenoble)45 (1995) 973-1006. Zbl0831.34023MR1359836
  6. [6] C. Imbert, J. Vovelle, A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications, SIAM, Mathematical Analysis, in press. Zbl1085.35099
  7. [7] Joseph K.T., LeFloch P.G., Boundary layers in weak solutions of hyperbolic conservation laws, Arch. Ration. Mech. Anal.147 (1999) 47-88. Zbl0959.35119MR1704856
  8. [8] Kružkov S.N., First order quasilinear equations with several independent variables, Mat. Sb. (N.S.)81 (123) (1970) 228-255. Zbl0215.16203MR267257
  9. [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. Zbl0354.35021MR483509
  10. [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. Zbl0820.35094MR1201239
  11. [11] Otto F., Initial-boundary value problem for a scalar conservation law, C. R. Acad. Sci. Paris Sér. I Math.322 (1996) 729-734. Zbl0852.35013MR1387428
  12. [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. Zbl0919.35088MR1661021
  13. [13] Tadmor E., Tang T., Pointwise error estimates for relaxation approximations to conservation laws, SIAM J. Math. Anal.32 (2000) 870-886, (electronic). Zbl0979.35098MR1814742
  14. [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. MR1871175

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