Optimal error estimates for semidiscrete phase relaxation models
M2AN - Modélisation mathématique et analyse numérique, Volume 31 (1997) no. 1, pp. 91-120.
@article{M2AN_1997__31_1_91_0,
     author = {Jiang, Xun and Nochetto, Ricardo H.},
     title = {Optimal error estimates for semidiscrete phase relaxation models},
     journal = {M2AN - Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {91--120},
     publisher = {Elsevier},
     volume = {31},
     number = {1},
     year = {1997},
     zbl = {0874.65069},
     mrnumber = {1432853},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1997__31_1_91_0/}
}
TY  - JOUR
AU  - Jiang, Xun
AU  - Nochetto, Ricardo H.
TI  - Optimal error estimates for semidiscrete phase relaxation models
JO  - M2AN - Modélisation mathématique et analyse numérique
PY  - 1997
DA  - 1997///
SP  - 91
EP  - 120
VL  - 31
IS  - 1
PB  - Elsevier
UR  - http://archive.numdam.org/item/M2AN_1997__31_1_91_0/
UR  - https://zbmath.org/?q=an%3A0874.65069
UR  - https://www.ams.org/mathscinet-getitem?mr=1432853
LA  - en
ID  - M2AN_1997__31_1_91_0
ER  - 
%0 Journal Article
%A Jiang, Xun
%A Nochetto, Ricardo H.
%T Optimal error estimates for semidiscrete phase relaxation models
%J M2AN - Modélisation mathématique et analyse numérique
%D 1997
%P 91-120
%V 31
%N 1
%I Elsevier
%G en
%F M2AN_1997__31_1_91_0
Jiang, Xun; Nochetto, Ricardo H. Optimal error estimates for semidiscrete phase relaxation models. M2AN - Modélisation mathématique et analyse numérique, Volume 31 (1997) no. 1, pp. 91-120. http://archive.numdam.org/item/M2AN_1997__31_1_91_0/

[1] T. Argogast, M. F. Wheeler and N. Y. Zhang, A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media, SIAM J. Numer. Anal, (to appear). | MR | Zbl

[2] C. Baiocchi, 1989, Discretization of evolution inequalities, in Partial Differential Equations and the Calculus of Variations, F. Colombini, A. Marino, M. Modica and S. Spagnolo eds, Birkäuser, Boston, pp. 59-92. | MR | Zbl

[3] J. W. Barrett and P. Knabner, Finite element approximation of transport of reactive solutes in porous media. Part 2 : Error estimates for equilibrium adsorption processes (to appear). | Zbl

[4] H. Brezis, 1971, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, in Contributions to Nonlinear Functional Analysis, E. Zarantonello ed., Academic Press, New York, pp. 101-156. | MR | Zbl

[5] M. G. Crandall and T. M. Liggett, 1971, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math., 93,pp. 265-298. | MR | Zbl

[6] X. Jiang and R. H. Nochetto, A P1-P1 finite element method for a phase relaxation model. Part I : Quasi-uniform mesh (to appear). | MR | Zbl

[7] E. Magenes, R. H. Nochetto and C. Verdi, 1987, Energy error estimates for a linear scheme to approximate nonlinear parabolic problems, RAIRO Model. Math. Anal. Numer., 21, pp, 655-678. | Numdam | MR | Zbl

[8] R. H. Nochetto, 1987, Error estimates for multidimensional singular parabolic problems, Japan J. Appl Math., 4, pp.111-138. | MR | Zbl

[9] R. H. Nochetto, 1991, Finite element methods for parabolic free boundary problems, in Advances in Numerical Analysis, Vol I: Nonlinear Partial Differential Equations and Dynamical Systems, W. Light ed., 1990 Lancaster Summer School Proceedings, Oxford University Press, pp. 34-88. | MR | Zbl

[10] R. H. Nochetto, M. Paolini and C. Verdi, 1994, Continuous and semidiscrete travelling waves for a phase relaxation model, European J. Appl. Math,, 5, pp. 177-199. | MR | Zbl

[11] R. H. Nochetto and C. Verdi, 1988, Approximation of degenerate parabolic problems using numerical integration, SIAM J. Numer. Anal., 25, pp. 784-814. | MR | Zbl

[12] J. Rulla, 1996, Error analysis for implicit approximations to solutions to Cauchy problems, SIAM J. Numer. Anal., 33, pp. 68-87. | MR | Zbl

[13] G. Savare, Weak solutions and maximal regularity for abstract evolution inequalities (to appear). | MR | Zbl

[14] C. Verdi, 1994, Numerical aspects of parabolic free boundary and hysteresis problems, in Phase Transitions and Hysteresis Phenomena, A. Vismtin (ed.). Springer-Verlag, Berlin, pp. 213-284. | MR | Zbl

[15] C. Verdi and A. Visintin, 1987, Numerical analysis of the multidimensional Stefan problem with supercooling and superheating, Boll Unione Mat. Ital. I-B, 7, pp. 795-814. | MR | Zbl

[16] C. Verdi and A. Visintin, 1988, Error estimates for a semi-explicit numerical scheme for Stefan-type problems, Numer. Math. 52, pp. 165-185. | MR | Zbl

[17] A. Visintin, 1985, Stefan problem with phase relaxation, IMA J. Appl. Math., 34,p. 225-245. | MR | Zbl

[18] A. Visintin, 1985, Supercooling and superheating effects in phase transitions,IMA J. Appl. Math., 35, pp 233-256. | MR | Zbl