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

Abstract

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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.

How to cite

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Barrett, 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 -

References

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