Finite volumes and nonlinear diffusion equations

R. Eymard; T. Gallouët; D. Hilhorst; Y. Naït Slimane

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1998)

  • Volume: 32, Issue: 6, page 747-761
  • ISSN: 0764-583X

How to cite

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Eymard, R., et al. "Finite volumes and nonlinear diffusion equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.6 (1998): 747-761. <http://eudml.org/doc/193896>.

@article{Eymard1998,
author = {Eymard, R., Gallouët, T., Hilhorst, D., Naït Slimane, Y.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nonlinear diffusion equations; nonlinear Stefan-type equation; convergence; finite volume methods},
language = {eng},
number = {6},
pages = {747-761},
publisher = {Dunod},
title = {Finite volumes and nonlinear diffusion equations},
url = {http://eudml.org/doc/193896},
volume = {32},
year = {1998},
}

TY - JOUR
AU - Eymard, R.
AU - Gallouët, T.
AU - Hilhorst, D.
AU - Naït Slimane, Y.
TI - Finite volumes and nonlinear diffusion equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 6
SP - 747
EP - 761
LA - eng
KW - nonlinear diffusion equations; nonlinear Stefan-type equation; convergence; finite volume methods
UR - http://eudml.org/doc/193896
ER -

References

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  4. [4] A. E. BERGER, H. BREZIS, J. C. W. ROGERS, A Numerical Method for Solving the Problem u1 - Δf(u) = 0, RAIRO Numerical Analysis, Vol. 13, 4, 297-312 (1979). Zbl0426.65052MR555381
  5. [5] M. BERTSCH, R. KERSNER, L. A. PELETIER, Positivity versus localization in degenerate diffusion equations, Nonlinear Analysis TMA, Vol. 9, 9, 987-1008 (1995). Zbl0596.35073MR804564
  6. [6] J. F. CIAVALDINI, Analyse numérique d'un problème de Stefan à deux phases par une méthode d'éléments finis, SIAM J. Numer. Anal., 12, 464-488 (1975). IAM J. Numer. Anal., 12, 464-488 (1975). Zbl0272.65101MR391741
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  8. [8] R. HERBIN, An error estimate for a finite volume scheme for a diffusion convection problem on a triangular mesh, Num. Meth. P.D.E., 165-173 (1995). Zbl0822.65085MR1316144
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  10. [10] O. A. LADYŽENSKAJA, V. A. SOLONNIKOV, N. N. URAL'CEVA, Linear and Quasilinear Equations of Parabolic Type, Transl. of Math. Monographs, 23 (1968). Zbl0174.15403MR241822
  11. [11] A. M. MEIRMANOV, The Stefan Problem, Walter de Gruyter Ed., New York (1992). Zbl0751.35052MR1154310
  12. [12] G. H. MEYER, Multidimensional Stefan Problems, SIAM J. Num. Anal., 10, 522-538 (1973). Zbl0256.65054MR331807
  13. [13] R. H. NOCHETTO, Finite Element Methods for Parabolic Free Boundary Problems, Advances in Numerical Analysis, Vol. I: Nonlinear Partial Differential Equations and Dynamical Systems, W. Light ed., Oxford University Press, 34-88 (1991). Zbl0733.65089MR1138471
  14. [14] O. A. OLEINIK, A method of solution of the general Stefan Problem, Sov. Math. Dokl. 1, 1350-1354 (1960). Zbl0131.09202MR125341
  15. [15] C. VERDI, Numerical aspects of parabolic free boundary and hysteresis problems, Phase Transitions and Hysteresis, A. Visinitin ed., Springer-Verlag, 213-284 (1994). Zbl0819.35155MR1321834

Citations in EuDML Documents

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  1. Kenneth Hvistendahl Karlsen, Nils Henrik Risebro, Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients
  2. Kenneth Hvistendahl Karlsen, Nils Henrik Risebro, Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients
  3. Robert Eymard, Raphaèle Herbin, Anthony Michel, Mathematical study of a petroleum-engineering scheme
  4. Robert Eymard, Raphaèle Herbin, Anthony Michel, Mathematical study of a petroleum-engineering scheme

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