A simple moving mesh method for one- and two-dimensional phase-field equations

A simple moving mesh method is proposed for solving phase-field equations. The numerical strategy is based on the approach proposed in Li et al. [J. Comput. Phys. 170 (2001) 562–588] to separate the mesh-moving and PDE evolution. The phase-field equations are discretized by a finite-volume method, and the mesh-moving part is realized by solving the conventional Euler–Lagrange equations with the standard gradient-based monitors. Numerical results demonstrate the accuracy and effectiveness of the proposed algorithm.