Stable phase field approximations of anisotropic solidification

Abstract

We introduce unconditionally stable finite element approximations for a phase
field model for solidification, which take highly anisotropic surface energy and kinetic
effects into account. We hence approximate Stefan problems with anisotropic
Gibbs{Thomson law with kinetic undercooling, and quasi-static variants thereof.
The phase field model is given by
#wt + � %(') 't = r: (b(')rw) ;
c
a
� %(')w = " �
� �(r') 't