Convergence of a finite-volume scheme for the Cahn-Hilliard equation with dynamic boundary conditions

Flore Nabet (1)

1 I2M - Institut de Mathématiques de Marseille

This work is devoted to the numerical study of the Cahn-Hilliard equation with dynamic boundary conditions. A spatial finite-volume discretization is proposed which couples a 2d-method in a smooth connected domain and a 1d-method on its boundary. The convergence of the sequence of approximate solutions is proved and various numerical simulations are given.

Mots clés: Cahn-Hilliard equation; Dynamic boundary conditions; Finite-volume method; Convergence analysis

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Flore Nabet. Convergence of a finite-volume scheme for the Cahn-Hilliard equation with dynamic boundary conditions. IMA Journal of Numerical Analysis, 2015, ⟨10.1093/imanum/drv057⟩. ⟨hal-01096996⟩