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Analysis of a finite element formulation for modelling phase separation

  • Garth N. Wells
  • Krishna Garikipati
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 5)

Summary

The Cahn-Hilliard equation is of importance in materials science and a range of other fields. It represents a diffuse interface model for simulating the evolution of phase separation in solids and fluids, and is a nonlinear fourth-order parabolic equation, which makes its numerical solution particularly challenging. To this end, a finite element formulation has been developed which can solve the Cahn-Hilliard equation in its primal form using C° basis functions. Here, analysis of a fully discrete version of this method is presented in the form of a priori uniqueness, stability and error analysis.

Keywords

Cahn-Hilliard equation discontinuous Galerkin method phase separation. 

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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Delft University of TechnologyDelftNetherlands
  2. 2.University of MichiganAnn ArborMichigan

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