| Issue |
ESAIM: M2AN
Volume 43, Number 3, May-June 2009
|
|
|---|---|---|
| Page(s) | 563 - 589 | |
| DOI | https://doi.org/10.1051/m2an/2009011 | |
| Published online | 30 April 2009 | |
Stability and convergence of two discrete schemes for a degenerate solutal non-isothermal phase-field model
Dpto. E.D.A.N., University of Sevilla,
Aptdo. 1160, 41080 Sevilla, Spain. guillen@us.es; juanvi@us.es
Received:
15
November
2007
Revised:
21
May
2008
Revised:
1
October
2008
We analyze two numerical schemes of Euler type in time and C0
finite-element type with 
-approximation in space for
solving a phase-field model of a binary alloy with thermal
properties. This model is written as a highly non-linear parabolic
system with three unknowns: phase-field, solute concentration and
temperature, where the diffusion for the temperature and solute
concentration may degenerate.
The first scheme is nonlinear, unconditionally stable
and convergent. The other scheme is linear but conditionally stable
and convergent. A maximum principle is avoided in both schemes,
using a truncation operator on the L2 projection onto the
finite element for the discrete concentration. In
addition, for the model when the heat conductivity and solute
diffusion coefficients are constants, optimal error estimates for
both schemes are shown based on stability estimates.
Mathematics Subject Classification: 35Q72 / 35K65 / 65M12 / 65M60
Key words: Phase-field models / diffuse interface model / solidification process / degenerate parabolic systems / backward Euler schemes / finite elements / stability / convergence / error estimates.
© EDP Sciences, SMAI, 2009
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