TY - JOUR
T1 - A Second-Order Energy Stable BDF Numerical Scheme for the Viscous Cahn-Hilliard Equation with Logarithmic Flory-Huggins Potential
AU - Wang , Danxia
AU - Wang , Xingxing
AU - Jia , Hongen
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 867
EP - 891
PY - 2021
DA - 2021/04
SN - 13
DO - http://doi.org/10.4208/aamm.OA-2020-0123
UR - https://global-sci.org/intro/article_detail/aamm/18755.html
KW - Viscous Cahn-Hilliard, logarithmic potential, BDF scheme, error estimates.
AB - <p style="text-align: justify;">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.</p>