The Sharpness Condition for Constructing Finite Element From a Superspline
In this talk, I will discuss the sharpness conditions for constructing Cʳ conforming finite element spaces from superspline spaces on general simplicial triangulations and introduce the concept of extendability for pre-element spaces, which unifies both superspline and finite element spaces under a common framework.
Overview
By examining the extendability condition for both, I will present precise criteria governing the construction of such elements. As a key result, we find that building Cʳ conforming elements in d-dimensional domains generally requires an additional $C^{2^{s - 1} r}$ continuity on s-codimensional subsimplices, and that the polynomial degree must be at least 2ᵈr+1.
Presenters
Qingyu Wu, Ph.D. Student, Mathematics, Peking University
Brief Biography
Qingyu Wu is a Ph.D. student at Peking University, supervised by Prof. Jun Hu. Her research explores finite element methods, especially the construction of high-order smooth elements in high-dimensional spaces. Her work has appeared in Foundations of Computational Mathematics and Mathematics of Computation.
