@Article{AAMM-13-867, author = {Wang , DanxiaWang , Xingxing and Jia , Hongen}, title = {A Second-Order Energy Stable BDF Numerical Scheme for the Viscous Cahn-Hilliard Equation with Logarithmic Flory-Huggins Potential}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {13}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0123}, url = {http://global-sci.org/intro/article_detail/aamm/18755.html} }