讲座主题：Two positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard-type equation

主讲人： 张争茹

工作单位：北京师范大学

活动时间：2020年12月8日 14：10-15：00

讲座地点：腾讯会议，会议ID：403 206 190

主办单位：烟台大学数学与信息科学学院

内容摘要：

In this work, two energy stable numerical schemes were proposed for the MMC-TDGL equation, a Cahn-Hilliard equation with a Flory-Huggins-deGennes energy. The main objective is focused on the bound estimate and convergence analysis of the unconditionally energy-stable schemes. We provide a theoretical justification of the unique solvability for the proposed numerical schemes, in which a well-known difficulty associated with the singular nature of the logarithmic energy potential has to be handled. Meanwhile, a careful analysis reveals that, such a singular nature prevents the numerical solution of the phase variable reaching the limit singular values, so that the positivity-preserving property could be proved at a theoretical level. In particular, the natural structure of the deGennes diffusive coefficient also ensures the desired positivity-preserving property. In turn, the unconditional energy stability becomes an outcome of the unique solvability and the convex-concave decomposition for the energy functional. Moreover, the optimal rate convergence analysis is presented for the two proposed schemes. Some numerical results are presented as well.

主讲人介绍：

2004年从香港浸会大学毕业并获得理学博士学位后在北京师范大学工作至今，现在的研究方向为偏微分方程数值计算，时间空间自适应方法，梯度流问题的分析与计算。在SIAM J. Sci. Comput., J. Comput. Phys., Computers & Fluids, Commun. Comput. Phys.等国际期刊已发表学术论文20多篇，主持完成国家自然科学基金多项，现正主持国家自然科学基金一项。