Report Title：Finite Element Complexes with Traces Structures: A unified framework for cohomology and bounded interpolation
Reporter：Liang Yizhou, PhD
Affiliation: University of Oxford
Report Time:10:30-11:30 January 7,2026
Report Location: Seminar Room 5, Wu Zhuoqun Building
University Contact: Zhang Qian (qzhang25@jlu.edu.cn)
Abstract:
We consider the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite element exterior calculus, the main challenge is the existence of extra smoothness. This paper provides a unified framework for finite element complexes with extra smoothness. The trace structure is introduced to derive the bubble complexes in different dimensions (vertices, edges, faces).
It is shown that if the bubble complexes in different dimensions are all exact, then the finite element has the correct cohomology. Moreover, the L^2 bounded interpolation can be constructed.
Bio:
Dr. Liang Yizhou is currently a postdoctoral researcher in the Department of Mathematics at the University of Oxford. He obtained his PhD from Peking University in 2022 and subsequently served as a Humboldt Scholar at the University of Augsburg, Germany, from 2022 to 2024. His research focuses on the numerical analysis of partial differential equation solutions, with a particular emphasis on Finite Element Exterior Calculus (FEEC) and its applications in numerical relativity. Additionally, he has a keen interest in the numerical analysis of eigenvalue problems, including the Gross–Pitaevskii equation and biharmonic eigenvalue problems.
