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

John W. Barrett; James F. Blowey; Harald Garcke

- Volume: 35, Issue: 4, page 713-748
- ISSN: 0764-583X

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topBarrett, John W., Blowey, James F., and Garcke, Harald. "On fully practical finite element approximations of degenerate Cahn-Hilliard systems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.4 (2001): 713-748. <http://eudml.org/doc/194070>.

@article{Barrett2001,

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.},

author = {Barrett, John W., Blowey, James F., Garcke, Harald},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {phase separation; multi-component systems; degenerate parabolic systems of fourth order; finite element method; convergence analysis; degenerate mobility matrix},

language = {eng},

number = {4},

pages = {713-748},

publisher = {EDP-Sciences},

title = {On fully practical finite element approximations of degenerate Cahn-Hilliard systems},

url = {http://eudml.org/doc/194070},

volume = {35},

year = {2001},

}

TY - JOUR

AU - Barrett, John W.

AU - Blowey, James F.

AU - Garcke, Harald

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

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

PY - 2001

PB - EDP-Sciences

VL - 35

IS - 4

SP - 713

EP - 748

AB - 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.

LA - eng

KW - phase separation; multi-component systems; degenerate parabolic systems of fourth order; finite element method; convergence analysis; degenerate mobility matrix

UR - http://eudml.org/doc/194070

ER -

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