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Unisolvence of Symmetric Node Patterns for Polynomial Spaces on the Simplex.
- Source :
- Journal of Scientific Computing; May2023, Vol. 95 Issue 2, p1-25, 25p
- Publication Year :
- 2023
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08857474
- Volume :
- 95
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Scientific Computing
- Publication Type :
- Academic Journal
- Accession number :
- 162665387
- Full Text :
- https://doi.org/10.1007/s10915-023-02161-1