报告题目：Conditions for constructing Cr finite elements

报告时间：2025-03-22  09:30-10:30

报 告 人：林挺   博士  北京大学

报告地点：雷军科技楼八楼报告厅（806）

Abstract：In finite element methods, C^rconforming finite elements can be used to solve high-order elliptic equations. When constructing C^rconforming finite elements on general triangulations, extra smoothness is imposed on lower - dimensional faces such as vertices and edges. For example, when constructing C^1planar finite elements, C^2data 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^rfinite elements in ddimensions. 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 ons-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.Thiswork is based on joint work with Jun Hu (Peking University), QingyuWu (Peking University), and BeihuiYuan (BIMSA).