Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-28T18:58:48.668Z Has data issue: false hasContentIssue false
  • English
  • Français

Continuous and semidiscrete travelling waves for a phase relaxation model

Published online by Cambridge University Press:  26 September 2008

Ricardo H. Nochetto ,
Maurizio Paolini  and
Claudio Verdi
Ricardo H. Nochetto
Affiliation:
Department of Mathematics and Institute of Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
Maurizio Paolini
Affiliation:
Dipartimento di Matemalica, Università di Milano, Via Saldini 50, 20133 Milano, and Istituto di Analisi Numerica del CNR, Corso Carlo Alberto 5, 21700 Pavia, Italy
Claudio Verdi
Affiliation:
Dipartimento di Matemalica, Università di Milano, Via Saldini 50, 20133 Milano, and Istituto di Analisi Numerica del CNR, Corso Carlo Alberto 5, 21700 Pavia, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

Quite precise asymptotic estimates, in terms of the relaxation parameter and the time step, are derived for travelling wave solutions to a Stefan problem with phase relaxation and a semidiscrete counterpart. These estimates quantify the regularizing effects of phase relaxation and time discretization that give rise to thin transition layers as opposed to sharp interfaces. Layer width estimates, pointwise error estimates, and asymptotic expressions for the profile of the relevant physical variables are proved. Applications to a related nonlinear Chernoff formula are also given.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 2 , June 1994 , pp. 177 - 199
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Jennings, G. 1974 Discrete shocks. Comm. Pure Appl. Math. 27, 25–37.CrossRefGoogle Scholar
[2]Magenes, E., Nochetto, R. H. & Verdi, C. 1987 Energy error estimates for a linear scheme to approximate nonlinear parabolic problems. RAIRO Modél. Math. Anal. Numér. 21, 655–678.Google Scholar
[3]Nochetto, R. H., Paolini, M. & Verdi, C. 1991 An adaptive finite elements method for two-phase Stefan problems in two-space dimensions. Part 1: stability and error estimates. Math. Comp. 57, 73–108; Supplement. Math. Comp. 57, Sl–S11.Google Scholar
[4]Nochetto, R. H., Paolini, M. & Verdi, C. 1992 Towards a unified approach for the adaptive solution of evolution phase changes. In Variational and Free Boundary Problems (ed. Friedman, A. & Spruck, J.) IMA VMA 53. Springer-Verlag. (To appear.)Google Scholar
[5]Nochetto, R. H., Paolini, M. & Verdi, C. 1992 A fully discrete adaptive nonlinear Chernoff formula. SIAM J. Numer. Anal. (To appear.)Google Scholar
[6]Verdi, C. & Visintin, A. 1988 Error estimates for a semiexplicit numerical scheme for Stefantype problems. Numer. Math. 52, 165–185.CrossRefGoogle Scholar
[7]Visintin, A. 1985 Stefan problem with phase relaxation. IMA J. Appl. Math. 34, 225–245.Google Scholar