We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham e-Theses
You are in:

Numerical analysis of a coupled pair of Cahn-Hilliard equations with non-smooth free energy

Sripirom, Pisuttawan (2007) Numerical analysis of a coupled pair of Cahn-Hilliard equations with non-smooth free energy. Doctoral thesis, Durham University.



A mathematical analysis has been carried out for a coupled pair of Cahn-Hilliard equations with a double well potential function with infinite walled free energy, which appears in modelling a phase separation on a thin film of binary liquid mixture coating substrate, which is wet by one component. Existence and uniqueness are proved for a weak formulation of the problem, which possesses a Lyapunov functional. Regularity results for the weak formulation are presented. Semi and fully discrete finite element approximations are proposed where existence and uniqueness of their solutions are proven. Their convergence to the solution of the continuous solutions are presented. Error bound between semi-discrete and continuous solutions, between semi-discrete and fully discrete solutions, and between fully discrete and continuous solutions are all investigated. A practical algorithm to solve the fully discrete finite element formulation at each time step is introduced and its convergence is shown. Finally, a linear stability analysis of the equations in one dimension space is presented and some numerical simulations in one and two dimension spaces are preformed.

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Thesis Date:2007
Copyright:Copyright of this thesis is held by the author
Deposited On:08 Sep 2011 18:31

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitter