报 告 人:李晓丽教授 山东大学
报告题目:EnergyStability and Error Analysis of High-precision Algorithms for theCahn-Hilliard-Navier-Stokes model
报告时间:2022年4月15日下午3:00-4:00
报告地点:腾讯会议 ID:524936343
主办单位:数学与统计学院、科学技术研究院
报告人简介:
李晓丽,山东大学教授,博士生导师,山东大学齐鲁青年学者。主要研究领域为偏微分方程数值解与计算流体力学。在SIAM J. Numer. Anal., Math. Comput., SIAM J. Sci. Comput., J. FluidMech., Math. Mod. Meth. Appl. Sci.等计算及应用数学顶级期刊上发表学术论文40余篇。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,山东省优秀博士学位论文,山东省研究生优秀科技成果二等奖等。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中国博士后科学基金一等资助。
报告摘要:
In this talk, we will first presentconstruction and analysis of an efficient numerical scheme based on the scalarauxiliary variable (SAV) and marker and cell scheme (MAC) for theCahn-Hilliard-Navier-Stokes model. A rigorous error analysis is carried out toshow that both velocity and pressure approximations are second-order accuratein time and space. Next we shall discuss how to construct new first- andsecond-order pressure correction schemes using the SAV approach. These schemesare linear, decoupled and only require solving a sequence of Poisson typeequations at each time step. We carry out a rigorous error analysis for thefirst-order scheme, establishing optimal convergence rate for all relevantfunctions in different norms. We also provide numerical experiments to verifyour theoretical results.
邀请人:侯典明、张超