Geodesic
Analysis of a time discretization scheme for a nonstandard viscous Cahn-Hilliard system
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 1061-1087

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In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase fields are the order parameter and the chemical potential. The initial and boundary-value problem for the evolutionary system is known to be well posed. Convergence of the discrete scheme to the solution of the continuous problem is proved by a careful development of uniform estimates, by weak compactness and a suitable treatment of nonlinearities. Moreover, for the difference of discrete and continuous solutions we prove an error estimate of order one with respect to the time step.

DOI : 10.1051/m2an/2014005
Classification : 35A40, 35K55, 35Q70, 65M12, 65M15
Keywords: Cahn-Hilliard equation, phase field model, time discretization, convergence, error estimates 
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     author = {Colli, Pierluigi and Gilardi, Gianni and Krej\v{c}{\'\i}, Pavel and Podio-Guidugli, Paolo and Sprekels, J\"urgen},
     title = {Analysis of a time discretization scheme for a nonstandard viscous {Cahn-Hilliard} system},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1061--1087},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {4},
     year = {2014},
     doi = {10.1051/m2an/2014005},
     mrnumber = {3264346},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2014005/}
}
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%A Podio-Guidugli, Paolo
%A Sprekels, Jürgen
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Colli, Pierluigi; Gilardi, Gianni; Krejčí, Pavel; Podio-Guidugli, Paolo; Sprekels, Jürgen. Analysis of a time discretization scheme for a nonstandard viscous Cahn-Hilliard system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 4, pp. 1061-1087. doi: 10.1051/m2an/2014005

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