Finite volume schemes for a nonlinear hyperbolic equation. Convergence towards the entropy solution and error estimate

Claire Chainais-Hillairet

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 1, page 129-156
  • ISSN: 0764-583X

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Chainais-Hillairet, Claire. "Finite volume schemes for a nonlinear hyperbolic equation. Convergence towards the entropy solution and error estimate." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.1 (1999): 129-156. <http://eudml.org/doc/193907>.

@article{Chainais1999,
author = {Chainais-Hillairet, Claire},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {finite volume method; error estimate; nonlinear conservation laws; convergence; entropy solution},
language = {eng},
number = {1},
pages = {129-156},
publisher = {Dunod},
title = {Finite volume schemes for a nonlinear hyperbolic equation. Convergence towards the entropy solution and error estimate},
url = {http://eudml.org/doc/193907},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Chainais-Hillairet, Claire
TI - Finite volume schemes for a nonlinear hyperbolic equation. Convergence towards the entropy solution and error estimate
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 1
SP - 129
EP - 156
LA - eng
KW - finite volume method; error estimate; nonlinear conservation laws; convergence; entropy solution
UR - http://eudml.org/doc/193907
ER -

References

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  1. [1] B. Cockburn, F. Coquel and P. Lefloch, An error estimate for finite volume methods for multidimensional convervation laws. Math. Comp. 63 (1994) 77-103. Zbl0855.65103MR1240657
  2. [2] R. Eymard, T. Gallouët, M. Ghilani and R. Herbin, Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by some finite volume schemes. IMA. J. Numer. Anal. 18 (1998) 563-594. Zbl0973.65078MR1681074
  3. [3] R. Eymard, T. Gallouët and R. Herbin, Convergence of a finite volume seheme for a nonlinear hyperbolic equation, Proceedings of the Third colloquium on numerical analysis, edited by D. Bainov and V. Covachev. Elsevier (1995) 61-70. Zbl0843.65068MR1455950
  4. [4] R. Eymard, T. Gallouët and R. Herbin, Existence and uniqueness of the entropy solution to a nonlinear hyperboiic equation. Chin. Ann. Math. B16 (1995) 1-14. Zbl0830.35077MR1338923
  5. [5] S. N. Kruskov, First order quasilinear equations with several space variable. Math. USSR. Sb. 10 (1970) 217-243. Zbl0215.16203
  6. [6] R. Di Perna, Measure-valued solutions to conservation laws. Arch. Rat. Mech Anal. 88 (1985) 223-270. Zbl0616.35055MR775191
  7. [7] R. J. Le Veque, Numerical methods for conservations laws. Birkhaeuser (1990). Zbl0723.65067MR1077828
  8. [8] J.P. Vila, Convergence and error estimate in finite volume schemes for gênerai multidimensional conservation laws. RAIRO Model. Math. Anal. Num. 28 (1994) 267-285. Zbl0823.65087MR1275345

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