讲座主题：Stability and error estimation based on a difference-spectral approximation for Cahn-Hilliard equation in complex domains

专家姓名：安静

工作单位：贵州师范大学

讲座时间：2025年05月07日14:00-15:00

讲座地点：数学院大会议室341

主办单位：烟台大学数学与信息科学学院

内容摘要：

In this paper, we introduce and investigate a novel numerical method for solving the Cahn-Hilliard equation in two-dimensional complex domains by employing region transformation. Initially, we convert the fourth-order equation into a second-order coupled system and formulate its first- and second-order semi-implicit schemes. Afterwards, we transform them into the polar coordinates equivalents. By introducing a category of weighted Sobolev spaces, we elaborate on fully discrete schemes and offer a theoretical validation of their stability. In particular, the introduction of pole singularities and the nonlinearity of the coupling problem pose significant challenges to theoretical analysis. To address these challenges, we introduce a novel class of projection operators and establish their approximation properties. Leveraging these properties, we provide error estimates for the approximate solutions. To validate our theoretical insights and algorithm's efficacy, we conclude with a series of numerical examples.

主讲人介绍：

安静，贵州师范大学教授，博士生导师，主持完成国家自然科学基金项目3项，在研国家自然科学基金项目1项，在SIAM J NUMER ANAL、J SCI COMPUT、APPL NUMER MATH等期刊发表SCI学术论文30余篇。