A Second-Order Energy Stable BDF Numerical Scheme for the Viscous Cahn-Hilliard Equation with Logarithmic Flory-Huggins Potential
Year: 2021
Author: Danxia Wang, Xingxing Wang, Hongen Jia
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 867–891
Abstract
In this paper, a viscous Cahn-Hilliard equation with logarithmic Flory-Huggins energy potential is solved numerically by using a convex splitting scheme. This numerical scheme is based on the Backward Differentiation Formula (BDF) method in time and mixed finite element method in space. A regularization procedure is applied to logarithmic potential, which makes the domain of the regularized function $F(u)$ to be extended from $(-1,1)$ to $(-\infty,\infty)$. The unconditional energy stability is obtained in the sense that a modified energy is non-increasing. By a carefully theoretical analysis and numerical calculations, we derive discrete error estimates. Subsequently, some numerical examples are carried out to demonstrate the validity of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0123
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 4 : pp. 867–891
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Viscous Cahn-Hilliard logarithmic potential BDF scheme error estimates.
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