The Willmore energy has widespread applications in differential geometry, cell membranes, optical lenses, materials science, among others. The Willmore flow, as the $L^2$ gradient flow dissipating the Willmore energy, serves as a fundamental tool for its analysis. Despite its importance, the development of energy-stable parametric methods for the Willmore flow remains open. In this talk, I will present a novel energy-stable numerical approximation for the Willmore flow. I begin by introducing our method for planar curves, then demonstrating the underlying ideas -- the new transport equation and the time derivative of the mean curvature, that ensure energy stability. Finally, we discuss the extension of our approach to surfaces in 3D.
李逸飞，2019年获北京大学本科学位，2023年获新加坡国立大学博士学位。现为德国图宾根大学洪堡博士后研究员。研究兴趣主要集中在几何流保结构算法，固态去湿问题的计算。
