学术报告:A convergent evolving finite element algorithm for mean curvature flow of closed surfaces

题目:A convergent evolving finite element algorithm for mean curvature flow of closed surfaces

主讲人:李步扬 Hong Kong Polytechnic University,Assistant Professor

日期:2018年11月29日(星期四)

时间:上午10:30-11:20

地点:数据科学与计算机学院 A203

主持:张庆辉 教授

摘要:A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the discrete surface like in {Dziuk's} method, and linearly implicit backward difference formulae for time integration. The proposed method differs from Dziuk's approach in that it discretizes Huisken's evolution equations for the normal vector and mean curvature and uses these evolving geometric quantities in the velocity law projected to the finite element space. This numerical method admits a convergence analysis, which combines stability estimates and consistency estimates to yield optimal-order H^1-norm error bounds for the computed surface position, velocity, normal vector and mean curvature. The stability analysis is based on the matrix--vector formulation of the finite element method and does not use geometric arguments. The geometry enters only into the consistency estimates. Numerical experiments illustrate and complement the theoretical results.

个人介绍:李步扬博士于 2005 年在山东大学取得数学学士学位,并分别于 2007、2009 及 2012 年在香港城市大学取得应用数学硕士、哲学硕士及博士学位。李博士于 2012 年 12 月开始任职于南京大学,并于 2015 年 7 月晋升为副教授。在 2015 年 6 月至 2016 年 5 月期间,李步扬博士并为德国图宾根大学兼任洪堡学者的工作。李步扬博士于 2016 年 6 月加入香港理工大学应用数学系担任助理教授一职。李步扬博士当前的主要研究兴趣是偏微分方程的数值解法和数值分析,在SIAM J. Numer. Anal., SIAM J. Sci. Comput., Math. Comput.,Numer. Math.  等计算数学顶级期刊上发表论文40多篇。