A linear extrapolation method for a general phase relaxation problem
- Volume: 7, Issue: 3, page 169-179
- ISSN: 1120-6330
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topJiang, Xun. "A linear extrapolation method for a general phase relaxation problem." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 7.3 (1996): 169-179. <http://eudml.org/doc/244327>.
@article{Jiang1996,
abstract = {This paper examines a linear extrapolation time-discretization of a \( 2D \) phase relaxation model with temperature dependent convection and reaction. The model consists of a diffusion-advection PDE for temperature and an ODE with double obstacle \( \pm 1 \) for phase variable. Under a stability constraint, this scheme is shown to converge with optimal orders \( \mathcal\{O\} (\tau | \log \tau |^\{1/2\}) \) for temperature and enthalpy, and \( \mathcal\{O\} (\tau^\{1/2\} | \log \tau |^\{1/2\}) \) for heat flux as time-step \( \tau \downarrow 0 \).},
author = {Jiang, Xun},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Phase relaxation; Stefan problem; Error estimate; Semi-implicit; Extrapolation; error estimate; semi-implicit; extrapolation; time-discretization; 2D phase relaxation model; diffusion-advection},
language = {eng},
month = {12},
number = {3},
pages = {169-179},
publisher = {Accademia Nazionale dei Lincei},
title = {A linear extrapolation method for a general phase relaxation problem},
url = {http://eudml.org/doc/244327},
volume = {7},
year = {1996},
}
TY - JOUR
AU - Jiang, Xun
TI - A linear extrapolation method for a general phase relaxation problem
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/12//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 3
SP - 169
EP - 179
AB - This paper examines a linear extrapolation time-discretization of a \( 2D \) phase relaxation model with temperature dependent convection and reaction. The model consists of a diffusion-advection PDE for temperature and an ODE with double obstacle \( \pm 1 \) for phase variable. Under a stability constraint, this scheme is shown to converge with optimal orders \( \mathcal{O} (\tau | \log \tau |^{1/2}) \) for temperature and enthalpy, and \( \mathcal{O} (\tau^{1/2} | \log \tau |^{1/2}) \) for heat flux as time-step \( \tau \downarrow 0 \).
LA - eng
KW - Phase relaxation; Stefan problem; Error estimate; Semi-implicit; Extrapolation; error estimate; semi-implicit; extrapolation; time-discretization; 2D phase relaxation model; diffusion-advection
UR - http://eudml.org/doc/244327
ER -
References
top- BERGER, A. E. - BREZIS, H. - ROGERS, J. C. W., A numerical method for solving the problem . RAIRO Anal. Numér., 1979, 297-312. Zbl0426.65052MR555381
- GILBARG, D. - TRUDINGER, N. S., Elliptic Partial Differential Equations of Second Order. 2nd ed., Springer, Berlin-Heidelberg1983. Zbl0361.35003MR737190
- JIANG, X. - NOCHETTO, R. H., Optimal error estimates for a semidiscrete phase relaxation model. RAIRO Model. Math. Anal. Numer., to appear. Zbl0874.65069MR1432853
- MAGENES, E. - NOCHETTO, R. H. - VERDI, C., Energy error estimates for a linear scheme to approximate nonlinear parabolic problems. RAIRO Model. Math. Anal. Numer., 21, 1987, 655-678. Zbl0635.65123MR921832
- NOCHETTO, R. H., Error estimates for multidimensional singular parabolic problems. Japan J. Appl. Math., 4, 1987, 111-138. Zbl0657.65132MR899207DOI10.1007/BF03167758
- NOCHETTO, R. H., Finite element methods for parabolic free boundary problems. In: W. LIGHT (ed.), Advances in Numerical Analysis, Vol. I: Nonlinear Partial Differential Equations and Dynamical Systems. 1990 Lancaster Summer School Proceedings, Oxford University Press, 1991, 34-88. Zbl0733.65089MR1138471
- NOCHETTO, R. H. - PAOLINI, M. - VERDI, C., Continuous and semidiscrete travelling waves for a phase relaxation model. European J. Appl. Math., 5, 1994, 177-199. Zbl0812.35166MR1285038DOI10.1017/S095679250000139X
- NOCHETTO, R. H. - VERDI, C., An efficient linear scheme to approximate parabolic free boundary problems: error estimates and implementation. Math. Comp., 51, 1988, 27-53. Zbl0657.65131MR942142DOI10.2307/2008578
- RULLA, J., Error analysis for implicit approximations to solutions to Cauchy problems. SIAM J. Numer. Anal, 33, 1996, 31-55. Zbl0855.65102MR1377244DOI10.1137/0733005
- VERDI, C., Numerical aspects of parabolic free boundary and hysteresis problems. In: A. VISINTIN (ed.), Phase Transition and Hysteresis. LN Math., vol. 158, Springer-Verlag, Berlin1994. Zbl0819.35155MR1321834DOI10.1007/BFb0073398
- VERDI, C. - VISINTIN, A., Error estimates for a semi-explicit numerical scheme for Stefan-type problems. Numer. Math., 52, 1988, 165-185. Zbl0617.65125MR923709DOI10.1007/BF01398688
- VISINTIN, A., Stefan problem with phase relaxation. IMA J. Appl. Math., 34, 1985, 225-245. Zbl0585.35053MR804824DOI10.1093/imamat/34.3.225
- VISINTIN, A., Supercooling and superheating effects in phase transition. IMA J. Appl. Math., 35, 1985, 233-256. Zbl0615.35090MR839201DOI10.1093/imamat/35.2.233
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