# Analysis of a time discretization scheme for a nonstandard viscous Cahn–Hilliard system

Pierluigi Colli; Gianni Gilardi; Pavel Krejčí; Paolo Podio-Guidugli; Jürgen Sprekels

- Volume: 48, Issue: 4, page 1061-1087
- ISSN: 0764-583X

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topColli, Pierluigi, et al. "Analysis of a time discretization scheme for a nonstandard viscous Cahn–Hilliard system." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.4 (2014): 1061-1087. <http://eudml.org/doc/273110>.

@article{Colli2014,

abstract = {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.},

author = {Colli, Pierluigi, Gilardi, Gianni, Krejčí, Pavel, Podio-Guidugli, Paolo, Sprekels, Jürgen},

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

keywords = {Cahn–Hilliard equation; phase field model; time discretization; convergence; error estimates},

language = {eng},

number = {4},

pages = {1061-1087},

publisher = {EDP-Sciences},

title = {Analysis of a time discretization scheme for a nonstandard viscous Cahn–Hilliard system},

url = {http://eudml.org/doc/273110},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Colli, Pierluigi

AU - Gilardi, Gianni

AU - Krejčí, Pavel

AU - Podio-Guidugli, Paolo

AU - Sprekels, Jürgen

TI - Analysis of a time discretization scheme for a nonstandard viscous Cahn–Hilliard system

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

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 4

SP - 1061

EP - 1087

AB - 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.

LA - eng

KW - Cahn–Hilliard equation; phase field model; time discretization; convergence; error estimates

UR - http://eudml.org/doc/273110

ER -

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