A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions | Zendy

Laurence Cherfils | Zendy; Mădălina Petcu | Zendy; Morgan Pierre | Zendy

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A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions

Author(s) -

Laurence Cherfils,

Mădălina Petcu,

Morgan Pierre

Publication year - 2010

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2010.27.1511

Subject(s) - discretization , cahn–hilliard equation , backward euler method , mathematics , convergence (economics) , boundary (topology) , stability (learning theory) , allen–cahn equation , finite element method , euler method , boundary value problem , mathematical analysis , space (punctuation) , scheme (mathematics) , euler's formula , partial differential equation , computer science , physics , machine learning , economics , thermodynamics , economic growth , operating system

We consider a finite element space semi-discretization of the Cahn- Hilliard equation with dynamic boundary conditions. We prove optimal error estimates in energy norms and weaker norms, assuming enough regularity on the solution. When the solution is less regular, we prove a convergence result in some weak topology. We also prove the stability of a fully discrete prob- lem based on the backward Euler scheme for the time discretization. Some numerical results show the applicability of the method.

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