报告题目 (Title)：Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential （具有对数势的Cahn-Hilliard 方程的保正且能量稳定的数值格式）
报告人 (Speaker)： 王成 教授（University of Massachusetts Dartmouth）
报告时间 (Time)：2023年12月27日(周三）10:00-11:00
报告地点 (Place)：校本部A104
邀请人(Inviter)：段成华
主办部门：永利数学系
报告摘要：
The Cahn-Hilliard model with logarithmic potential is considered, in which the key difficulty has always been associated with the singularity of the logarithmic terms. An energy stable finite difference scheme, which implicitly treats the logarithmic terms, is proposed and analyzed in this talk. In particular, how to ensure the positivity of the logarithmic arguments, so that the numerical scheme is well-defined at a point-wise level, has been a long-standing mathematical challenge. It is proved that, given any numerical solution with a fixed bound at the previous time step, there exists a unique numerical solution that satisfies the given bound (-1,1) at a point-wise level. As a result, the numerical scheme is proven to be well-defined, and the unique solvability and energy
stability could be established with the help of convexity analysis. In addition, an optimal rate convergence analysis could be appropriately established. Some numerical results are also presented in the talk.
