哈尔滨工业大学（深圳）学术讲座

演讲人Speaker：   希腊约阿尼拉大学 Georgios Akrivis  教授

题目Title: Quadratic Constraint Consistency in the Projection-Free Approximation of Harmonic Maps and Bending Isometries

时间Date：2023年 11 月 22 日       Time：16:00–17:00

地点Venue：H403

内容摘要Abstract： 

After recalling the notion of harmonic maps into spheres, we discuss two variational formulations of the corresponding Euler–Lagrange equations. The second variational formulation leads easily to a linearization of the nonlinear equation. Subsequently, we focus on the gradient flow approach and recall known results for the linearly implicit Euler method, namely, energy decay (stability) and constraint violation properties.

Our contribution concerns the application of the linearly implicit two-step BDF method to the gradient flow problem. More precisely, we devise a projection-free iterative scheme for the approximation of harmonic maps that provides a second-order accuracy of the constraint violation and is unconditionally energy stable. A corresponding error estimate is valid under a mild but necessary discrete regularity condition. The considered problem serves as a model for partial differential equations with holonomic constraint.

For the performance of the method, illustrated via the computation of stationary harmonic maps and bending isometries, we refer to the manuscript on which the talk is based.

个人简介(About the speaker):

讲座主讲人信息：Georgios Akrivis，希腊约阿尼拉大学教授。Akrivis 教授于1983年获得德国慕尼黑大学博士学位，曾在克里特大学担任助理教授和副教授，并于1995年加入约阿尼拉大学。他的研究兴趣是线性和非线性演化偏微分方程的数值方法和分析，在SIAM Journal on Numerical Analysis，Numerische Mathematik，Mathematics of Computation等杂志发表SCI论文70余篇。现为SIAM Journal on Numerical Analysis 编委。