一、题目

High-order finite element methods for time-moving interface problems

二、主讲人

郑伟英

三、摘要

We propose a high-order unfitted finite element method to solve moving interface problem of the Oseen equations. The purpose is to present a thorough error estimates for discrete solutions by taking full considerations of errors from interface-tracking, temporal discretization, and spatial discretization. In literatures on interface problems of time-dependent Stokes equations, error estimates for the discrete pressure are usually studied under the L^2-norm and are sub-optimal. We have obtained optimal error estimates for the pressure under H^1-norm by introducing proper interior penalties to the discrete problem. Optimal error estimates for the discrete velocity are also obtained with convergence orders 2≤k≤4. Numerical experiments for a severely deforming interface showthat optimal convergence orders are obtained for k = 3 and 4.

四、主讲人介绍

郑伟英，中国科学院数学与系统科学研究院研究员，长期从事电磁场和流体计算研究，在Maxwell方程自适应多重网格方法、分层介质散射问题的计算方法和理论、磁流体计算等方面取得重要科研进展。2019 年被聘为中科院数学与系统科学研究院“冯康首席研究员”，2021年获冯康科学计算奖。

五、邀请人

蒋晓芸 数学学院教授

六、时间

11月22日（周一）14:30

七、地点

腾讯会议ID：847 191 015

八、主办方

山东大学数学学院