Numerical Approximations and Error Analysis of the Cahn-Hilliard Equation with Dynamic Boundary Conditions
Numerical Analysis
2020-10-14 v2 Numerical Analysis
Abstract
We consider the numerical approximations of the Cahn-Hilliard equation with dynamic boundary conditions (C. Liu et. al., Arch. Rational Mech. Anal., 2019). We propose a first-order in time, linear and energy stable numerical scheme, which is based on the stabilized linearly implicit approach. The energy stability of the scheme is proved and the semi-discrete-in-time error estimates are carried out. Numerical experiments, including the comparison with the former work, the accuracy tests with respect to the time step size and the shape deformation of a droplet, are performed to validate the accuracy and the stability of the proposed scheme.
Keywords
Cite
@article{arxiv.2006.05391,
title = {Numerical Approximations and Error Analysis of the Cahn-Hilliard Equation with Dynamic Boundary Conditions},
author = {Xuelian Bao and Hui Zhang},
journal= {arXiv preprint arXiv:2006.05391},
year = {2020}
}