The Nodal Basis of $C^m-P(3,k)$ and $C^m-P(4,k)$ Finite Elements on Tetrahedral and 4D Simplicial Grids

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 $C^m-P(4,k).$

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Publication Details

Journal
East Asian Journal on Applied Mathematics
Published
2026-05-30
DOI
https://doi.org/10.4208/eajam.2025-110.211025
Primary Topic
Numerical methods in engineering
Type
preprint
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0.00
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preprint

The Nodal Basis of $C^m-P(3,k)$ and $C^m-P(4,k)$ Finite Elements on Tetrahedral and 4D Simplicial Grids

Shangyou Zhang
East Asian Journal on Applied Mathematics
Numerical methods in engineering
preprint

The Nodal Basis of $C^m-P(3,k)$ and $C^m-P(4,k)$ Finite Elements on Tetrahedral and 4D Simplicial Grids

Shangyou Zhang
preprint en

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 $C^m-P(4,k).$

East Asian Journal on Applied Mathematics
University of Delaware (US)
Openalex Percentile: Top 100%
Numerical methods in engineering
DOIOpen Access PDFOpenAlex
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The Nodal Basis of $C^m-P(3,k)$ and $C^m-P(4,k)$ Finite Elements on Tetrahedral and 4D Simplicial Grids — Shangyou Zhang · East Asian Journal on Applied Mathematics (2026) | TGRS Research Map | TGRS