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• W4328129752 abstract "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." @default.
• W4328129752 created "2023-03-22" @default.
• W4328129752 creator A5054099820 @default.
• W4328129752 date "2023-03-21" @default.
• W4328129752 modified "2023-10-01" @default.
• W4328129752 title "Unisolvence of Symmetric Node Patterns for Polynomial Spaces on the Simplex" @default.
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• W4328129752 doi "https://doi.org/10.1007/s10915-023-02161-1" @default.
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