Error estimates for the Cahn--Hilliard equation with dynamic boundary conditions
Numerical Analysis
2020-12-01 v3 Numerical Analysis
Abstract
A proof of convergence is given for bulk--surface finite element semi-discretisation of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak formulation as a second order system. Optimal-order uniform-in-time error estimates are shown in the and norms. The error estimates are based on a consistency and stability analysis. The proof of stability is performed in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second order system. Numerical experiments illustrate the theoretical results.
Cite
@article{arxiv.2005.03349,
title = {Error estimates for the Cahn--Hilliard equation with dynamic boundary conditions},
author = {Paula Harder and Balázs Kovács},
journal= {arXiv preprint arXiv:2005.03349},
year = {2020}
}