An error estimate for a finite-volume scheme for the Cahn-Hilliard equation with dynamic boundary conditions

Flore Nabet (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

In the paper we consider a finite-volume approximation for the Cahn-Hilliard equation with dynamic boundary conditions. We prove an error estimate for the fully-discrete scheme. The convergence of the scheme is proved in Nabet (IMA J Numer Anal 36(4): 1898–1942, 2016), we prove here an error estimate for the fully-discrete scheme. We also give numerical simulations which validate the theoretical result.

Mots clés: Cahn-Hilliard equation; dynamic boundary condition; finite-volume method; error estimate

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

Flore Nabet. An error estimate for a finite-volume scheme for the Cahn-Hilliard equation with dynamic boundary conditions. Numerische Mathematik, 2021, 149 (1), pp.185-226. ⟨10.1007/s00211-021-01230-7⟩. ⟨hal-01273945v3⟩