报告主题: Parametric finite element methods for geometric flows
报 告 人: 苏春梅助理教授
报告时间: 2024年6月27日(星期四)下午16:00-17:00
报告地点: 37号楼3A02
邀 请 人: 姚文琦 副教授
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数学学院
2024年 6月20日
报告摘要:
This talk includes two parts. (1) Firstly we present and analyze a semi-discrete parametric finite element scheme for solving 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.
报告人介绍:
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。目前已在国际重要期刊如 SlAM Journal on Numerical Analysis, SlAM Journal on Scientific Computing, Multiscale Modeling & Simulation, Numerische Mathematik, Mathematics of Computation, Foundations of Computational Mathematics, Journal of Computational Physics 等发表论文三十余篇。