Unisolvence of Symmetric Node Patterns for Polynomial Spaces on the Simplex

W. A. Mulder*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
48 Downloads (Pure)

Abstract

Finite elements with polynomial basis functions on the simplex with a symmetric distribution of nodes should have a unique polynomial representation. Unisolvence not only requires that the number of nodes equals the number of independent polynomials spanning a polynomial space of a given degree, but also that the Vandermonde matrix controlling their mapping to the Lagrange interpolating polynomials can be inverted. Here, a necessary condition for unisolvence is presented for polynomial spaces that have non-decreasing degrees when going from the edges and the various faces to the interior of the simplex. It leads to a proof of a conjecture on a necessary condition for unisolvence, requiring the node pattern to be the same as that of the regular simplex.

Original languageEnglish
Article number45
Number of pages25
JournalJournal of Scientific Computing
Volume95
Issue number2
DOIs
Publication statusPublished - 2023

Keywords

  • Finite elements
  • Node patterns
  • Polynomial
  • Simplex
  • Unisolvence

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