Locally generated C¹-splines over triangular meshes

2019/03/27 by László L. Stachó, Stachó, Laszlo
Engineering · Mathematics · #41A15 #65D07 #65D15 #Advanced Numerical Analysis Techniques #Composite Structure Analysis and Optimization #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1903.11336

openalex publication_date 2019/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We classify all possible local linear procedures over triangular meshes resulting in polynomial C¹-spline functions with affinely uniform shape for the basic functions at the edges, and fitting the 9 value- and gradient data at the vertices of the mesh members. There is a unique procedure among them with shape functions and basic polynomials of degree 5 and all other admissible procedures are its perturbations with higher degree.

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