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On fully practical finite element approximationsof degenerate Cahn-Hilliard systems

Published online by Cambridge University Press:  15 April 2002

John W. Barrett ,
James F. Blowey  and
Harald Garcke
John W. Barrett
Affiliation:
Department of Mathematics, Imperial College, London, SW7 2BZ, UK. (j.barrett@ic.ac.uk)
James F. Blowey
Affiliation:
Department of Mathematical Sciences, University of Durham, DH1 3LE, UK.
Harald Garcke
Affiliation:
Institut für Angewandte Mathematik, Wegelerstraße 6, 53115 Bonn, Germany.
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Abstract

We consider a model for phase separation of a multi-component alloy with non-smooth free energyand a degenerate mobility matrix. In addition to showingwell-posedness and stability bounds for our approximation, we prove convergence in one space dimension. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. We discuss also how our approximation has to be modified in orderto be applicable to a logarithmic free energy.Finally numerical experiments with three components in one and two space dimensions are presented.

Keywords

Phase separationmulti-component systemsdegenerateparabolic systems of fourth orderfinite element methodconvergence analysis.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 4 , July 2001 , pp. 713 - 748
Copyright
© EDP Sciences, SMAI, 2001

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