Share:


On fully discrete Galerkin approximations for the Cahn‐Hilliard equation

    K. Omrani Affiliation

Abstract


Standard Galerkin approximations, using smooth splines to solutions of the nonlinear evolutionary Cahn‐Hilliard equation are analysed. The existence, uniqueness and convergence of the fully discrete Crank‐Nicolson scheme are discussed. At last a linearized Galerkin approximation is presented, which is also second order accurate in time fully discrete scheme.


Pilnai diskrečioji Galerkino aproksimacija Cahn-Hilliard lygčiai


Santrauka. Straipsnyje analizuojama standartinė Galerkino aproksimacija nestacionariajai Canh‐Hilliard lygčiai, panaudojant glodžius splainus. Aptarta pilnai diskrečios Cranko‐Nikolsono baigtinių skirtumų schemos sprendinio egzistencija, vienatis ir konvergavimas. Pabaigoje pateikta tiesinė Galerkino diskrečioji schema, kuri yra antros eilės tikslumo pagal laika.



First Published Online: 14 Oct 2010

Keyword : Cahn‐Hilliard equation, Galerkin scheme, convergence, linearization

How to Cite
Omrani, K. (2004). On fully discrete Galerkin approximations for the Cahn‐Hilliard equation. Mathematical Modelling and Analysis, 9(4), 313-326. https://doi.org/10.3846/13926292.2004.9637262
Published in Issue
Dec 31, 2004
Abstract Views
389
PDF Downloads
217
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.