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(xué)
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(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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(xué)畢業(yè)并獲得理學(xué)博士學(xué)位后在北京師范大學(xué)工作至今,，現(xiàn)在的研究方向為偏微分方程數(shù)值計算，時間空間自適應(yīng)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(fā)表學(xué)術(shù)論文20多篇,，主持完成國家自然科學(xué)基金多項，現(xiàn)正主持國家自然科學(xué)基金一項,。
