ESAIM: Mathematical Modelling and Numerical Analysis

Table of Contents - November 1999 - Volume 33, Issue 06  

Research Article

A class of time discrete schemes for a phase–field system of Penrose–Fife type

Klein, Olaf

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany. klein@wias-berlin.de.

Abstract

In this paper, a phase field system of Penrose–Fife type with non–conserved order parameter is considered. A class of time–discrete schemes for an initial–boundary value problem for this phase–field system is presented. In three space dimensions, convergence is proved and an error estimate linear with respect to the time–step size is derived.

(Received August 28 1998)

(Revised April 2 1999)

(Online publication August 15 2002)

Key Words:

  • Phase–field model;
  • Penrose–Fife model;
  • semidiscretization;
  • convergence;
  • error estimates.

Mathematics Subject Classification:

  • 65M12;
  • 35K50;
  • 80A22;
  • 35K60;
  • 35R35;
  • 65M15