Anisotropic mesh adaptation for the solution of the Stefan problem

A new finite element formulation for the solution of the classical Stefan problem is introduced. It is obtained by a slight modification of the phase-field formulation used for dendritic growth where both the phase-field φ and the temperature T are discretized. An anisotropic mesh adaptation strategy is also presented to further increase the accuracy of the method. Numerical results for two-dimensional examples illustrating the performance and accuracy of the proposed method are presented.