Speaker: Dr. Lixiu Dong （董丽秀博士）

Time: 10:00-11:00, 26 July 2024 (Friday) (Beijing time)

Tencent Meeting ID:767-953-4082

Abstract

In this talk, a ternary Cahn-Hilliard system with a Flory-Huggins-deGennesfree energy potential is considered, in which the key diffculty has alwaysbeen associated with the singularity ofthe logarithmic terms. An energy stablefnite difference scheme based on the convex splitting method, whichimplicitly treats the logarithmic terms, is proposed and analyzed in this talkWe provide a theoretical justification that this numerical scheme has a pair ofunique solutions, such that the positivity is always preserved for all thesingular 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-wiselevel. As a result, the numerical scheme is proven to be well-defined, and theunique solvability and energy stability could be established with the help ofconvexity analysis. In addition, an optimal rate convergence analysis could beappropriately established. Some numerical results are also presented.

About Dr. Dong

董丽秀，博士毕业于北京师范大学，现任北京师范大学珠海校区文理学院数学系讲师、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，主要成果发表在JCP，JCAM.CICP等期刊，其中WebofScience中高引论文一篇。现主持国家自然科学基金青年基金项目，参与国家自然科学基金面上G纮睃谐靶项目1项。