An r-Adaptive Finite Element Method for the Solution of the Two-Dimensional Phase-Field Equations

An adaptive moving mesh method is developed for the numerical solutionof two-dimensional phase change problems modelled by the phase-field equations. Thenumerical algorithm is relatively simple and is shown to be more efficient than fixed gridmethods. The phase-field equations are discretized by a Galerkin finite element method.An adaptivity criterion is used that ensures that the mesh spacing at the phase frontscales with the diffuse interface thickness.