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arXiv · 2006.05391

Numerical Approximations and Error Analysis of the Cahn-Hilliard Equation with Dynamic Boundary Conditions

Xuelian Bao·Hui Zhang
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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.

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Xuelian Bao, Hui Zhang. 2020-06-09. Numerical Approximations and Error Analysis of the Cahn-Hilliard Equation with Dynamic Boundary Conditions. https://arxiv.org/abs/2006.05391

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