Error estimates for semi-discrete dendritic growth

Abstract

Semi-discrete approximations to a mathematical model for two-dimensional dendritic growth are analysed. The model is a Stefan problem with interfacial structure. The semi-discrete problem uses a parametrization for the free boundary and finite elements in space. The main results are a priori error estimates for the temperature field and the parametrization of the free boundary. The optimality of their order is discussed. Further error estimates concern approximations to relevant geometric (e.g. curvature) and measuring quantities.