講座主題：Error Analysis and Numerical Simulations of High-Precision Finite Difference Algorithms for Complex Dissipative Systems
主持人：李曉麗
工作單位：廈門大學(xué)
講座時間：2019年12月7日（周六）下午15:30--16:10
講座地點：數(shù)學(xué)院341
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 talk, we shall first present construction and analysis of a block-centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank-Nicolson scheme (SAV/CN-BCFD) for gradient flows, and show rigorously that scheme is second-order in both time and space in various discrete norms. When equipped with an adaptive time strategy, the SAV/CN-BCFD scheme is accurate and extremely efficient. Then we will discuss how to construct a numerical scheme based on the SAV approach in time and the MAC discretization in space for the Cahn-Hilliard-Navier-Stokes phase field model, and carry out stability and error analysis. We also present the recent work on the SAV approach for the Navier-Stokes equations. Finally the numerical simulations are demonstrated the robustness and accuracy of our scheme.
主講人介紹：
李曉麗， 廈門大學(xué)博士后,，合作導(dǎo)師沈捷教授,。2018年12月山東大學(xué)博士畢業(yè)，主要研究領(lǐng)域為偏微分方程數(shù)值解與計算流體力學(xué),，已在SIAM J. Numer. Anal., Math. Comput., Comput. Methods Appl. Mech. Engrg.等計算數(shù)學(xué)高水平期刊上發(fā)表學(xué)術(shù)論文30余篇,，其中以第一作者或通訊作者發(fā)表25篇。獲得中國工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會第16屆年會優(yōu)秀學(xué)生論文獎,，山東省研究生優(yōu)秀科技成果二等獎,。2019年入選“博士后創(chuàng)新人才支持計劃”，獲國家自然科學(xué)青年基金以及第65批中國博士后科學(xué)基金一等資助,。
