报告题目：Parametric finite element methods for geometric flows

报 告 人：苏春梅助理教授（清华大学丘成桐数学科学中心）

报告时间：2024年7月29日  10:30-11:30

报告地点：数学研究中心528

报告摘要：

This talk includes two parts. (1) Firstly we present and analyze a semi-discrete parametric finite element scheme for solying the area-preserving curve shortening flow. The scheme is based on Dziuk's approach (SIAM J. Numer. Anal. 36(6): 1808-1830, 1999) for the anisotropic curve shortening flow. We prove that the scheme preserves two fundamental geometric structures of the flow with an initially convex curve: (i) the convexity-preserving property, and (ii) the perimeter-decreasing property. To the best of our knowledge, the convexity-preserving property of numerical schemes which approximate the flow is rigorously proved for the first time. Furthermore, the error estimate of the semi-discrete scheme is established, and numerical results are provided to demonstrate the structure-preserving properties as well as the accuracy of the scheme. (2) To avoid the clustering of nodes in the simulation of Dziuk's type schemes, we present some high-order methods based on the BGN formulation, which achieve high-order accuracy in time and exhibit good properties with respect to the mesh distribution.

报告人简介：

苏春梅，2015年博士毕业于北京大学，此后先后在北京计算科学研究中心、新加坡国立大学、因斯布鲁克大学、慕尼黑工业大学做博士后研究。2021年被聘为清华大学丘成桐数学科学中心助理教授，研究方向为偏微分方程数值解，近年来主要研究色散类方程及高振荡方程的计算方法及其分析。已在国际重要期刊如SIAM J. Numer. Anal., SIAM J. Sci. Comput., Numer. Math., Math. Comput., Found. Comput. Math., J. Comput. Phys.等发表SCI论文三十余篇。