The Nodal Basis of $C^m$-$P^{(3)}_k$ and $C^m$-$P^{(4)}_k$ Finite Elements on Tetrahedral and 4D Simplicial Grids
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 $C^m$-$P^{(4)}_k.$
Fields of Study & Subjects
Numerical methods in engineering
Matrix Theory and Algorithms
Electromagnetic Scattering and Analysis
Publication details
- Journal / source
- East Asian Journal on Applied Mathematics
- Publisher
- Global Science Press
- Volume
- 17
- Issue
- 1
- Pages
- 95–104
- Publication date
- 30 May 2026
- Language
- EN