A Multi-Mesh Adaptive Finite Element Approximation to Phase Field Models (Communications in Computational Physics, 2009)
In this work, we propose an efficient multi-mesh adaptive finite elementmethod for simulating the dendritic growth in two- and three-dimensions. The governing equations used are the phase field model, where the regularity behaviors of therelevant dependent variables, namely the thermal field function and the phase fieldfunction, can be very different. To enhance the computational efficiency, we approximate these variables on different h-adaptive meshes. The coupled terms in the systemare calculated based on the implementation of the multi-mesh h-adaptive algorithmproposed by Li (J. Sci. Comput., pp. 321-341, 24 (2005)). It is illustrated numericallythat the multi-mesh technique is useful in solving phase field models and can savestorage and the CPU time significantly.