Geodesic
On fully practical finite element approximations of degenerate Cahn-Hilliard systems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 4, pp. 713-748

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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.

Classification : 35K35, 35K55, 35K65, 65M12, 65M60, 82C26
Keywords: phase separation, multi-component systems, degenerate parabolic systems of fourth order, finite element method, convergence analysis 
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     author = {Barrett, John W. and Blowey, James F. and Garcke, Harald},
     title = {On fully practical finite element approximations of degenerate {Cahn-Hilliard} systems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {713--748},
     publisher = {EDP-Sciences},
     volume = {35},
     number = {4},
     year = {2001},
     mrnumber = {1863277},
     zbl = {0987.35071},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/M2AN_2001__35_4_713_0/}
}
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Barrett, John W.; Blowey, James F.; Garcke, Harald. On fully practical finite element approximations of degenerate Cahn-Hilliard systems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 35 (2001) no. 4, pp. 713-748. http://geodesic.mathdoc.fr/item/M2AN_2001__35_4_713_0/