报告题目：High-order Finite Element Methods for Time-moving Interface Problems
主 讲 人：郑伟英
腾 讯 ID：632 466 847
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 show that optimal convergence orders are obtained for k = 3 and 4.