Journal
MULTISCALE MODELING & SIMULATION
Volume 6, Issue 1, Pages 1-26Publisher
SIAM PUBLICATIONS
DOI: 10.1137/060656942
Keywords
phase field model; liquid-solid phase transition; homogenization; finite element method; a priori error estimate; multiscale model
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We present finite element error estimates for discretizations of a phase field model and a two-scale model. Both models describe solidi. cation with equiaxed dendritic microstructure. The two-scale model is a homogenization limit of the phase field model for periodic initial conditions of scale epsilon>0 under the assumption of a suitable scaling of physical parameters of the model. The scaling corresponds to a model with fast heat and slow solute diffusion, where the temperature is microscopically well mixed and the solute diffusion arises on the scale of single or few equiaxed crystals only. A comparison of the error estimates for both models is presented, showing that the two-scale model is superior if the mesh size for the macroscopic model is larger than epsilon(5/4) in an asymptotic sense.
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