Workshop on

numerical methods for multiscale problems

 

     
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  Eck: A finite element method for a two-scale phase field model

A finite element discretization for a two-scale phase field model describing solidification with equiaxed dendritic microstructure is discussed. The two-scale model represents a homogenization limit of a phase field model for the solidification of binary mixtures with periodic initial conditions under the assumption of small solute diffusion. It consists of a macroscopic heat transfer equation, involving an effective heat conductivity and an averaged release of latent heat; and of microscopic problems describing the evolution of single dendrites and the solute transport. Error estimates for discretizations of both the original model and the two-scale model are derived and compared.
Impressum
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