The Nodal Basis of $C^m$-$P^{(3)}_k$ and $C^m$-$P^{(4)}_k$ Finite Elements on Tetrahedral and 4D Simplicial Grids
Year: 2026
Type: article
Abstract: Let $C^m$-$P^{(n)}_k$ stand for the space of globally $C^m,$ $m≥1$ and locally piecewise $n$-dimensional polynomials of degree $k$ on $n$-dimensional simplicial grids. We construct bases of $C^m$-$P^{(3)}_k,$ $k≥2^3 m+1$ and $C^m$-$P^{(4)}_k,$ $k≥2^4 m+1$ finite elements on 3D tetrahedral and 4D simplicial grids, respectively, and prove the uni-solvency and the $C^m$ continuity of the finite element spaces $C^m-P^{(3)}_k$ and $C^m$-$P^{(4)}_k.$
Author: Shangyou Zhang
Institution: University of Delaware
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4221164992