講座主題：Stability and error estimation based on a difference-spectral approximation for Cahn-Hilliard equation in complex domains
專家姓名：安靜
工作單位：貴州師范大學(xué)
講座時(shí)間：2025年05月07日14:00-15:00
講座地點(diǎn)：數(shù)學(xué)院大會(huì)議室341
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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.
主講人介紹：
安靜，貴州師范大學(xué)教授，博士生導(dǎo)師，主持完成國(guó)家自然科學(xué)基金項(xiàng)目3項(xiàng)，在研國(guó)家自然科學(xué)基金項(xiàng)目1項(xiàng)，在SIAM J NUMER ANAL、J SCI COMPUT、APPL NUMER MATH等期刊發(fā)表SCI學(xué)術(shù)論文30余篇。
