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An optimal error bound for a finite element approximation of a model for phase separation of a multi-component alloy with non-smooth free energy

John W. BarrettJames F. Blowey — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

Using the approach in [5] for analysing time discretization error and assuming more regularity on the initial data, we improve on the error bound derived in [2] for a fully practical piecewise linear finite element approximation with a backward Euler time discretization of a model for phase separation of a multi-component alloy with non-smooth free energy.

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

John W. BarrettJames F. BloweyHarald Garcke — 2001

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

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

John W. BarrettJames F. BloweyHarald Garcke — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

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...

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