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

Authors:
Zhijun Tan;Tao Tang;Zhengru Zhang
Affiliations:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;School of Mathematical Sciences, Beijing Normal University, Beijing, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

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.