应用数学青年讨论班(午餐会)--Finite element form-valued forms: A unified construction
报告人：林挺(北京大学)
时间：2025-06-11 11:45-13:00
地点：智华楼四元厅
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).
报告人信息:
林挺，北京大学数学科学学院计算数学方向博士生。曾获北京大学未名学士，北京大学校长奖学金，东亚SIAM分会最佳论文奖一等奖等。2025年入选科协青年人才托举工程博士生专项。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Journal of the European Mathematical Society, Foundations of Computational Mathematics, Mathematics of Computation, Journal of Machine Learning Research, SIAM系列期刊等。
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