A numerical method for solving the problem u t - Δ f ( u ) = 0

Alan E. Berger; Haim Brezis; Joël C. W. Rogers

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1979)

  • Volume: 13, Issue: 4, page 297-312
  • ISSN: 0764-583X

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Berger, Alan E., Brezis, Haim, and Rogers, Joël C. W.. "A numerical method for solving the problem $u_t - \Delta f (u) = 0$." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 13.4 (1979): 297-312. <http://eudml.org/doc/193344>.

@article{Berger1979,
author = {Berger, Alan E., Brezis, Haim, Rogers, Joël C. W.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nonlinear evolution equations; stability; convergence; algorithm; numerical experiments},
language = {eng},
number = {4},
pages = {297-312},
publisher = {Dunod},
title = {A numerical method for solving the problem $u_t - \Delta f (u) = 0$},
url = {http://eudml.org/doc/193344},
volume = {13},
year = {1979},
}

TY - JOUR
AU - Berger, Alan E.
AU - Brezis, Haim
AU - Rogers, Joël C. W.
TI - A numerical method for solving the problem $u_t - \Delta f (u) = 0$
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1979
PB - Dunod
VL - 13
IS - 4
SP - 297
EP - 312
LA - eng
KW - nonlinear evolution equations; stability; convergence; algorithm; numerical experiments
UR - http://eudml.org/doc/193344
ER -

References

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  6. 6. A. E. BERGER, M. CIMENT and J. C. W. ROGERS, Numerical Solution of a Diffusion Consumption Problem with a Free Boundary, S.I.A.M. J. Numer. Anal., Vol. 12, 1975, pp. 646-672. Zbl0317.65032MR383779
  7. 7. A. E. BERGER, M. CIMENT and J. C. W. ROGERS, Numerical Solution of a Stefan Problem by a Technique of Alternating Phase Truncation, Séminaires IRIA, Analyse et contrôle des systèmes, Rocquencourt, Institut de Recherche d'Informatique et d'automatique, 1976, pp. 21-34. 
  8. 8. A. E. BERGER and R. S. FALK, An Error Estimate for the Truncation Method for the Solution of Parabolic Obstacle Variational Inequalities, Math. Comp., Vol. 31, 1977 pp. 619-628. Zbl0367.65056MR438707
  9. 9. H. BREZIS, On Some Degenerate Nonlinear Parabolic Equations, Nonlinear Functional Analysis, F. BROWDER, Ed., Proc. Symp. in pure math., Vol. 18, A.M.S., 1970, pp. 28-38. Zbl0231.47034MR273468
  10. 10. H. BREZIS and A. PAZY, Convergence and Approximation of Semigroups of Nonlinear Operators in Banach Spaces, J. Func. Anal., Vol. 9, 1972, pp. 63-74. Zbl0231.47036MR293452
  11. 11. H. BREZIS and W. A. STRAUSS, Semi-linear second-order elliptic equations in L 1 , J. Math. Soc. Japan, Vol. 25, 1973, pp. 565-590. Zbl0278.35041MR336050
  12. 12. M. G. CRANDALL, An Introduction to Evolution Governed by Accretive Operators, Dynamical systems vol. 1, Proc. of the Int. Symp. on Dyn. Sys. at Brown U. August 12-16, 1974, L. CESARI, J. K. HALE and J. P. LASALLE, Eds, New York, Academic Press, 1976, pp. 131-165. Zbl0339.35049MR636953
  13. 13. M. G. CRANDALL, Semigroups of Nonlinear Transformations in Banach Spaces, Contributions to nonlinear Functional Analysis, E. ZARANTONELLO, Ed., New York, Academic Press, 1971, pp. 157-179. Zbl0268.47066MR470787
  14. 14. M. G. CRANDALL and T. M. LIGGETT, Generation of Semi-groups of Nonlinear Transformations on General Banach Spaces, Amer. J. Math., Vol. 93, 1971, pp. 265-298. Zbl0226.47038MR287357
  15. 15. A. DAMLAMIAN, Some Results on the Multi-phase Stefan Problem, Comm. on P.D.E., Vol. 2, 1977, pp. 1017-1044. Zbl0399.35054MR487015
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  17. 17. B. H. GILDING and L. A. PELETIER, On a Class of Similarity Solutions of the Porous Media Equation, J. Math. Anal. Appl., Vol. 55, 1976, pp. 351-364. Zbl0356.35049MR436751
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  20. 20. J. C. W. ROGERS, A. E. BERGER and M. CIMENT, The Alternating Phase Truncation Method for Numerical Solution of a Stefan Problem, to appear in S.I.A.M. J. Num. Anal. Zbl0418.65051
  21. 21. M. ROSE, A Method for Calculating Solutions of Parabolic Equations with a Free Boundary, Math. Comp., Vol. 14, 1960, pp. 249-256. Zbl0096.10102MR115283

Citations in EuDML Documents

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  1. Enrico Magenes, Claudio Verdi, Augusto Visintin, Semigroup approach to the Stefan problem with non-linear flux
  2. E. Magenes, R. H. Nochetto, C. Verdi, Energy error estimates for a linear scheme to approximate nonlinear parabolic problems
  3. G. Amiez, P.-A. Gremaud, Error estimates for Euler forward scheme related to two-phase Stefan problems
  4. Akira Mizutani, Norikazu Saito, Takashi Suzuki, Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory
  5. R. Eymard, T. Gallouët, D. Hilhorst, Y. Naït Slimane, Finite volumes and nonlinear diffusion equations
  6. Akira Mizutani, Norikazu Saito, Takashi Suzuki, Finite element approximation for degenerate parabolic equations. an application of nonlinear semigroup theory
  7. Hideki Murakawa, A linear scheme to approximate nonlinear cross-diffusion systems
  8. Éric Boillat, An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
  9. Éric Boillat, An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
  10. Xun Jiang, A linear extrapolation method for a general phase relaxation problem

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