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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F14%3A00430395" target="_blank" >RIV/67985840:_____/14:00430395 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1051/m2an/2014005" target="_blank" >http://dx.doi.org/10.1051/m2an/2014005</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1051/m2an/2014005" target="_blank" >10.1051/m2an/2014005</a>

Result language
angličtina
Original language name
Analysis of a time discretization scheme for a nonstandard viscous Cahn-Hilliard system
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F10%2F2315" target="_blank" >GAP201/10/2315: Mathematical modeling of Processes in Hysteretic Materials</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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