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

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...

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Veröffentlicht in:	ESAIM. Mathematical modelling and numerical analysis 2001-07, Vol.35 (4), p.713-748
Hauptverfasser:	Barrett, John W., Blowey, James F., Garcke, Harald
Format:	Artikel
Sprache:	eng
Schlagworte:	35K35 35K55 35K65 65M12 65M60 82C26 Approximation convergence analysis degenerate parabolic systems of fourth order Energy Exact sciences and technology finite element method Mathematical analysis Mathematics multi-component systems Numerical analysis Numerical analysis. Scientific computation Partial differential equations Partial differential equations, initial value problems and time-dependant initial-boundary value problems Phase separation Phase transitions: general studies Physics Sciences and techniques of general use Statistical physics, thermodynamics, and nonlinear dynamical systems Thermodynamics
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Beschreibung
Zusammenfassung:	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.
ISSN:	0764-583X 1290-3841
DOI:	10.1051/m2an:2001133