@Article{CiCP-28-3,
author = {Lixiu, Dong and Wang, Cheng and Zhang, Hui and Zhengru, Zhang},
title = {A Positivity-Preserving Second-Order BDF Scheme for the Cahn-Hilliard Equation with Variable Interfacial Parameters},
journal = {Communications in Computational Physics},
year = {2020},
volume = {28},
number = {3},
pages = {967--998},
abstract = {<p style="text-align: justify;">We present and analyze a new second-order finite difference scheme for
the Macromolecular Microsphere Composite hydrogel, Time-Dependent Ginzburg-Landau (MMC-TDGL) equation, a Cahn-Hilliard equation with Flory-Huggins-deGennes energy potential. This numerical scheme with unconditional energy stability is based on the Backward Differentiation Formula (BDF) method in time derivation
combining with Douglas-Dupont regularization term. In addition, we present a pointwise bound of the numerical solution for the proposed scheme in the theoretical level.
For the convergent analysis, we treat three nonlinear logarithmic terms as a whole and
deal with all logarithmic terms directly by using the property that the nonlinear error
inner product is always non-negative. Moreover, we present the detailed convergent
analysis in $ℓ^∞$(0,$T$;$H_h^{-1}$)∩$ℓ^2$(0,$T$;<span style="text-align: justify;">$H_h^1$</span>)&nbsp; norm. At last, we use the local Newton approximation and multigrid method to solve the nonlinear numerical scheme, and various
numerical results are presented, including the numerical convergence test, positivity-preserving property test, spinodal decomposition, energy dissipation and mass conservation properties.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2019-0037},
url = {https://global-sci.com/article/79709/a-positivity-preserving-second-order-bdf-scheme-for-the-cahn-hilliard-equation-with-variable-interfacial-parameters}
}