报告题目：Finite element form-valued forms: A unified construction

报 告 人：林挺 博士 

所在单位：北京大学

报告时间：2025年7月8号，星期二，9点

报告地点：正新楼306

报告摘要：We provide a finite element discretization of $\ell$-form-valued $k$ form in $n$ dimensions for general $k$, $\ell$ and $n$ and polynomial degree. The construction generalizes finite element Whitney forms for the de~Rham complex and their higher-order and distributional versions, the Regge finite elements and the Christiansen--Regge elasticity complex, the TDNNS element for symmetric stress tensors, the MCS element for traceless matrix fields, the Hellan--Herrmann--Johnson (HHJ) elements for biharmonic equations, and discrete divdiv and Hessian complexes in [Hu, Lin, and Zhang, 2025]. The construction discretizes the Bernstein--Gelfand--Gelfand (BGG) diagrams. Applications of the construction include discretization of strain and stress tensors in continuum mechanics and metric and curvature tensors in differential geometry in any dimension. This talk is based on a joint work with Kaibo Hu (Edinburgh).

报告人简介：林挺，现为北京大学应用与计算数学专业的博士研究生，导师为胡俊教授。2021年获得北京大学数学与应用数学专业学士学位。研究方向包括有限元构造、有限元外微积分与有限元张量复型、控制理论与深度学习中的近似理论，以及弹性问题和微局部结构的数值分析。