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On fully practical finite element approximations of degenerate Cahn-Hilliard systems.

Barrett, J. W. and Blowey, J. F. and Garcke, H. (2001) 'On fully practical finite element approximations of degenerate Cahn-Hilliard systems.', ESAIM : mathematical modelling and numerical analysis = Modelisation mathematique et analyse numerique., 35 (4). pp. 713-748.

Abstract

We consider a model for phase separation of a multi-component alloy with non-smooth free energy and a degenerate mobility matrix. In addition to showing well-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 order to be applicable to a logarithmic free energy. Finally numerical experiments with three components in one and two space dimensions are presented.

Item Type:Article
Keywords:Phase separation, Multi-component systems, Degenerate parabolic systems of fourth order, Finite element method, Convergence analysis.
Full text:PDF - Published Version (2033Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1051/m2an:2001133
Publisher statement:© EDP Sciences, SMAI 2001
Record Created:24 Apr 2007
Last Modified:17 May 2010 16:08

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