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.
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
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