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

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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- 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 35.4 (2010): 713-748. <http://eudml.org/doc/197520>.

@article{Barrett2010,

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},

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

language = {eng},

month = {3},

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/197520},

volume = {35},

year = {2010},

}

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

DA - 2010/3//

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.; phase separation; convergence analysis; degenerate mobility matrix

UR - http://eudml.org/doc/197520

ER -

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## Citations in EuDML Documents

top- Franck Boyer, Sebastian Minjeaud, Numerical schemes for a three component Cahn-Hilliard model
- Franck Boyer, Sebastian Minjeaud, Numerical schemes for a three component Cahn-Hilliard model
- Pierluigi Colli, Gianni Gilardi, Pavel Krejčí, Paolo Podio-Guidugli, Jürgen Sprekels, Analysis of a time discretization scheme for a nonstandard viscous Cahn–Hilliard system

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