講座主題：Two positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard-type equation
主講人： 張爭茹
工作單位：北京師范大學
活動時間：2020年12月8日 14：10-15：00
講座地點：騰訊會議，會議ID：403 206 190
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
In this work, two energy stable numerical schemes were proposed for the MMC-TDGL equation, a Cahn-Hilliard equation with a Flory-Huggins-deGennes energy. The main objective is focused on the bound estimate and convergence analysis of the unconditionally energy-stable schemes. We provide a theoretical justification of the unique solvability for the proposed numerical schemes, in which a well-known difficulty associated with the singular nature of the logarithmic energy potential has to be handled. Meanwhile, a careful analysis reveals that, such a singular nature prevents the numerical solution of the phase variable reaching the limit singular values, so that the positivity-preserving property could be proved at a theoretical level. In particular, the natural structure of the deGennes diffusive coefficient also ensures the desired positivity-preserving property. In turn, the unconditional energy stability becomes an outcome of the unique solvability and the convex-concave decomposition for the energy functional. Moreover, the optimal rate convergence analysis is presented for the two proposed schemes. Some numerical results are presented as well.
主講人介紹：
2004年從香港浸會大學畢業并獲得理學博士學位后在北京師范大學工作至今，現在的研究方向為偏微分方程數值計算，時間空間自適應方法，梯度流問題的分析與計算。在SIAM J. Sci. Comput., J. Comput. Phys., Computers & Fluids, Commun. Comput. Phys.等國際期刊已發表學術論文20多篇，主持完成國家自然科學基金多項，現正主持國家自然科學基金一項。
