讲座主题：Error Analysis and Numerical Simulations of High-Precision Finite Difference Algorithms for Complex Dissipative Systems

主持人：李晓丽

工作单位：厦门大学

讲座时间：2019年12月7日（周六）下午15:30--16:10

讲座地点：数学院341

主办单位：烟台大学数学与信息科学学院

内容摘要：

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.

主讲人介绍：

李晓丽， 厦门大学博士后，合作导师沈捷教授。2018年12月山东大学博士毕业，主要研究领域为偏微分方程数值解与计算流体力学，已在SIAM J. Numer. Anal., Math. Comput., Comput. Methods Appl. Mech. Engrg.等计算数学高水平期刊上发表学术论文30余篇，其中以第一作者或通讯作者发表25篇。获得中国工业与应用数学学会第16届年会优秀学生论文奖，山东省研究生优秀科技成果二等奖。2019年入选“博士后创新人才支持计划”，获国家自然科学青年基金以及第65批中国博士后科学基金一等资助。