Locally generated $\mathcal{C}^1$-splines over triangular meshes
Numerical Analysis
2019-03-28 v1
Abstract
We classify all possible local linear procedures over triangular meshes resulting in polynomial -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.
Cite
@article{arxiv.1903.11336,
title = {Locally generated $\mathcal{C}^1$-splines over triangular meshes},
author = {Laszlo Stachó},
journal= {arXiv preprint arXiv:1903.11336},
year = {2019}
}