Communications in Mathematical Sciences
Volume 19 (2021)
Numerical approximations and error analysis of the Cahn–Hilliard equation with dynamic boundary conditions
Pages: 663 – 685
We consider the numerical approximations of the Cahn–Hilliard equation with dynamic boundary conditions [C. Liu et al., Arch. Ration. 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.
Cahn–Hilliard equation, dynamic boundary conditions, error estimates, linear numerical scheme, energy stability
2010 Mathematics Subject Classification
65M06, 65M12, 65M22, 65N12
X. Bao is partially supported by China Scholarship Council (No. 201906040019). H. Zhang was partially supported by the National Natural Science Foundation of China (Nos. 11971002 and 11471046).
Received 9 April 2020
Accepted 11 October 2020
Published 5 May 2021