Error estimates for semi-discrete dendritic growth (Q1971104)

The author presents the analysis of semi-discrete approximations to a mathematical model for two-dimensional dendritic growth. The model is a Stefan problem with a generalized Gibbs-Thompson law: \[ \theta_t- \Delta \theta =0 \quad \text{in }\omega^s(t)\cup \omega^l(t), \qquad v=-[\theta_n]^l _s \quad \text{on }\gamma(t), \] \[ \beta(n)v+\alpha(n)k +\theta=0\quad \text{ on }\gamma(t), \] \noindent where \(\omega^l\), \(\omega^s\) denote the liquid and solid regions respectively, which are separated by the interface \(\gamma\), \(\theta\) is temperature, \(n\) is normal and \(v\) is normal velocity. Besides \(\alpha\) and \(\beta \) denote material quantities. The main results are a priori error estimates for the parametrization of the free boundary and for the temperature field.