ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

16. Applications

1991 MS Classification: 35, 61 Klein, Olaf, Weierstrass Institute, Berlin, Germany Approximation results for phase–field systems In this talk, the following phase field system of Penrose–Fife type is considered

(c_{0}θ_{t} + λ(χ))_{t} + κ Δ (\frac{1}{θ}) = g,
δχ_{t} − εΔχ + β(χ) + σ′(χ) ∋ −\frac{λ′(χ)}{θ},

which models the evolution of the the absolute temperature θ and the order parameter χ during a phase transition. Here, β is a maximal monotone graph and λ and σ are quadratic functions. For the approximate solution of this problem, a time–discrete scheme is used. Convergence and an error estimate that is linear with respect to the time step size will be shown. Finally, numerical results will be presented.