報告題目：A positivity-preserving, energy stable and convergent numerical scheme for a ternary Cahn-Hilliard-type system
報 告 人：董麗秀 講師 北京師範大學珠海校區
報告時間：2023年 03月28日（星期 二）9:30-11:00
報告地點：騰訊會議: 291-385-427
校内聯系人：王翔 wxjldx@jlu.edu.cn
報告摘要：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.
報告人簡介：董麗秀，北京師範大學珠海校區，未來教育學院講師，碩士生導師，研究方向是偏微分方程數值解，主要從事梯度流問題特别是帶有奇性的多組分問題的數值方法和理論分析。參與國家自然科學基金面上項目若幹，主持國家自然科學基金青年基金項目，相關成果發表在Journal of Computational Physics，Communications in Computational Physics等國際知名期刊，其中Web of Science中高引論文一篇。
