Error estimate for approximate solutions of a nonlinear convection-diffusion problem

Advances in Differential Equations

Volumn 7, Issue 4, 2002, Pages 419-440

  Eymard, Robert ^a   Gallouët, Thierry ^b   Herbin, Raphaèle ^b  

^a UNIVERSITÉ GUSTAVE EIFFEL   (France)

^b UNIVERSITÉ DE PROVENCE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346115389     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. C. Bardos, A.Y. Leroux, and J.C. Nédélec, First order quasilinear equations with boundary conditions, Commun. Partial Differ. Eq., 4 (1979), 1017-1034.
2. Ph. Bénilan, Equations d'évolution dans un espace de Banach quelconque et applications, Thèse d'état, Université d'Orsay (1972).
3. F. Bouchut, F. Guarguaglini, and R. Natalini, Diffusive BGK approximations for nonlinear multidimensional parabolic equations, Indiana Univ. Math. J., 49 (2000).
4. H. Brezis "Analyse Fonctionnelle: Théorie et Applications", Masson, Paris, (1983).
5. J. Carrillo Entropy solutions for nonlinear degenerate problems, Arch. Rat. Mech. Anal., 147 (1999), 269-361.
6. B.Cockburn, F. Coquel, and P. LeFloch, An error estimate for finite volume methods for multidimensional conservation laws, Math. Comput., 63 (1994), 207, 77-103.
7. B. Cockburn and G. Gripenberg, Continuous dependence on the nonlinearities of solutions of degenerate parabolic equations, J. Differential Equations, 151 (1999), 231-251.
8. P. Dangla, O. Coussy, and R. Eymard, A vanishing diffusion process in unsaturated soils, Int. J. Non-Linear Mechanics, 33 (1998), 1027-1037.
9. R. DiPerna, Measure-valued solutions to conservation laws, Arch. Rat. Mech. Anal., 88 (1985), 223-270.
10. R. Eymard, Simulation of air-water flows in soils, First M.I.T. Conference on Computational Fluid and Solid Mechanics, June 12-14 (2001).
11. R. Eymard, T. Gallouët, and R. Herbin Existence and Uniqueness of the Entropy Solution to a Nonlinear Hyperbolic Equation. Chi. Ann. of Math., 16, Ser B 1 (1995), 1-14.
12. R. Eymard, T. Gallouët, M. Ghilani, and R. Herbin Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes. IMA Journal of Numerical Analysis, 18 (1997), 563-594.
13. R. Eymard, T. Gallouët, R. Herbin, and A. Michel, Convergence of a finite volume scheme to the entropy weak solution of a nonlinear hyperbolic degenerate parabolic equation, accepted for publication in Num. Math.
14. D. Kröner and M. Ohlberger, A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multi dimensions. Math. Comput., 69 (2000), 25-39.
15. S.N. Krushkov, First Order quasilinear equations with several space variables, Math. USSR. Sb., 10 (1970), 217-243.
16. A. Lagha-Benabdallah and F. Smadhi, Existence de solutions faibles pour un problème aux limites associé à une équation parabolique dégénérée, Maghreb Math. Rev., 2 (1993), 201-222.
17. B.A. Schrefler and D. Gawin, The effective stress principle: incremental or finite form?, Int. Jour. for Num. or Ana. Methods in Geomechanics, 20 (1996), 785-814.
18. J.P. Vila Convergence and error estimate in finite volume schemes for general multidimensional conservation laws, I. explicit monotone schemes, Model. Math. Anal. Numer., 28 (1994), 267-285.