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

Please always quote using this URN:urn:nbn:de:0296-matheon-12211
  • 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.

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Metadaten
Author:Pierluigi Colli, Gianni Gilardi, Pavel Krejcí, Podio-Guidugli Paolo, Sprekels Jürgen
URN:urn:nbn:de:0296-matheon-12211
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2015/12/23
Release Date:2015/12/23
Tag:Cahn--Hilliard equation; convergence; error estimates; phase field model; time discretization
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K55 Nonlinear parabolic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q70 PDEs in connection with mechanics of particles and systems
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M12 Stability and convergence of numerical methods
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M15 Error bounds
Preprint Number:1085
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