A numerical method for solving the problem
Alan E. Berger; Haim Brezis; Joël C. W. Rogers
- Volume: 13, Issue: 4, page 297-312
- ISSN: 0764-583X
Access Full Article
topHow to cite
topBerger, 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
top- 1. D. G. ARONSON, Regularity Properties of Flows through Porous Media, S.I.A.M., J. Appl. Math., Vol. 17, 1969, pp. 461-467. Zbl0187.03401MR247303
- 2. D. R. ATTHEY, A finite Difference Scheme for Melting Problems, J. Inst. Math. Appl., Vol. 13, 1974, pp. 353-366. MR351295
- 3. J. R. BAILLON and B. MERCIER, Convergence of Approximations to Nonlinear Semigroups, École Polytechnique Internal Report Number 24, December 1977.
- 4. Ph. BENILAN, Equations d'évolution dans un espace de Banach quelconque et applications, Thèse, Publications Mathématiques d'Orsay, n° 25, 1972.
- 5. A. E. BERGER, The Truncation Method for the Solution of a Class of Variational Inequalities, R.A.I.R.O., Analyse Numérique, Vol. 10, 1976, pp. 29-42. Zbl0334.49012MR455489
- 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. 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. 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. 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. 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. H. BREZIS and W. A. STRAUSS, Semi-linear second-order elliptic equations in , J. Math. Soc. Japan, Vol. 25, 1973, pp. 565-590. Zbl0278.35041MR336050
- 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. 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. 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. A. DAMLAMIAN, Some Results on the Multi-phase Stefan Problem, Comm. on P.D.E., Vol. 2, 1977, pp. 1017-1044. Zbl0399.35054MR487015
- 16. J. DOUGLAS Jr. and T. DUPONT, Alternating-Direction Galerkin Methods on Rectangles, Numerical Solution of Partial Differential Equations-II, SYNSPADE 1970, B. HUBBARD, Ed., New York, Academic press, 1971, pp. 133-214. Zbl0239.65088MR273830
- 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
- 18. B. H. GILDING and L. A. PELETIER, On a Class of Similarity Solutions of the Porous Media Equation II, J. Math. Anal. Appl., Vol. 57, 1977, pp. 522-538. Zbl0365.35029MR436752
- 19. D. W. PEACEMAN and H. H. RACHFORD Jr., The Numerical Solution of Parabolic and Elliptic Differential Equations, J. Soc. Indust. Appl. Math., Vol. 3, 1955, pp. 28-41. Zbl0067.35801MR71874
- 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. 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
top- Enrico Magenes, Claudio Verdi, Augusto Visintin, Semigroup approach to the Stefan problem with non-linear flux
- Enrico Magenes, Claudio Verdi, Augusto Visintin, Semigroup approach to the Stefan problem with non-linear flux
- E. Magenes, R. H. Nochetto, C. Verdi, Energy error estimates for a linear scheme to approximate nonlinear parabolic problems
- G. Amiez, P.-A. Gremaud, Error estimates for Euler forward scheme related to two-phase Stefan problems
- Akira Mizutani, Norikazu Saito, Takashi Suzuki, Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory
- R. Eymard, T. Gallouët, D. Hilhorst, Y. Naït Slimane, Finite volumes and nonlinear diffusion equations
- Molati, Motlatsi, Murakawa, Hideki, An efficient linear numerical scheme for the Stefan problem, the porous medium equation and nonlinear cross-diffusion systems
- Hideki Murakawa, A linear scheme to approximate nonlinear cross-diffusion systems
- Éric Boillat, An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
- Xun Jiang, A linear extrapolation method for a general phase relaxation problem
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.