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Center For Applied and Computational Mathematics

Finite Element Error Estimates for Phase Field Models

Dendritic Growth

Faculty: Baasansuren Jadamba


Phase field models are used to describe liquid solid phase transition processes such as casting of metals and alloys. We work on error estimates for a finite element discretization of phase field models for mixtures. The main focus of our work is on dependence of the error on a small parameter that represents the thickness of the transition layer between solid and liquid phases. An interesting application of phase field models is in dendritic microstructure growth at the solid-liquid interface. Simulation of the dendritic microstructures by a phase field model is facilitated by introduction of anisotropic surface tension in the free energy functional.


  1. Error Estimates for a Finite Element Discretization of a Phase Field Model for Mixtures, Ch. Eck, B. Jadamba, P.Knabner, SIAM J. Num. Anal., 47 (2010), 4429-4445.


Christof Eck (University of Stuttgart)
Peter Knabner (University of Erlangen-Nuremberg)