报告题目：A positivity-preserving, energy stable and convergent numerical scheme for a ternary Cahn-Hilliard-type system

报 告 人：董丽秀 讲师 北京师范大学珠海校区

报告时间：2023年 03月28日（星期 二）9:30-11:00

报告地点：腾讯会议: 291-385-427

校内联系人：王翔 wxjldx@jlu.edu.cn

报告摘要：In this talk, a ternary Cahn-Hilliard system with a Flory-Huggins-deGennes free energy 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. We provide a theoretical justification that this numerical scheme has a pair of unique solutions, such that the positivity is always preserved for all the singular terms, i.e., not only two phase variables are always between 0 and 1, but also the sum of two phase variables is between 0 and 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.

报告人简介：董丽秀，北京师范大学珠海校区，未来教育学院讲师，硕士生导师，研究方向是偏微分方程数值解，主要从事梯度流问题特别是带有奇性的多组分问题的数值方法和理论分析。参与国家自然科学基金面上项目若干，主持国家自然科学基金青年基金项目，相关成果发表在Journal of Computational Physics，Communications in Computational Physics等国际知名期刊，其中Web of Science中高引论文一篇。