报告人：林挺（北京大学）

时 间：2025年1月14日（星期二），下午2:00-4:00

地 点：海纳苑2幢205

摘 要：In finite element methods, $C^r$ conforming finite elements can be used to solve high-order elliptic equations. When constructing $C^r$ conforming finite elements on general triangulations, extra smoothness is imposed on lower - dimensional faces such as vertices and edges. For example, when constructing $C^1$ planar finite elements, $C^2$ data at vertices is utilized.

In this talk, we explore the sufficient and necessary conditions for constructing \(C^r\) conforming elements. For the sufficient condition, we present a unified construction for $C^r$ finite elements in $d$ dimensions. This construction requires that the polynomial degree be greater than $2^{d + 1}r$ and that $ 2^{d - s}r\$ of extra smoothness be imposed on $s$-dimensional faces. Regarding the necessary condition, we demonstrate that the requirements are in fact sharp, meaning they cannot be relaxed. Furthermore, some interesting connections among finite elements, splines, and algebraic methods will also be explored and discussed. This work is based on joint work with Jun Hu (Peking University), Qingyu Wu (Peking University), and Beihui Yuan (BIMSA).

报告人简介：林挺是北京大学博士生，导师为胡俊教授。曾获北京大学未名学士，东亚SIAM分会最佳论文奖一等奖等。主要研究方向为有限元方法与深度学习中的逼近论，相关论文发表于J. Eur. Math. Soc, Found Comut Math, SIAM系列, JMLR 等.