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

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

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

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

Abstract

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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.

How to cite

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Colli, 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 -

References

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