Locally generated Hermitian C1-splines on triangular meshes

Abstract

We classify all possible local linear procedures on triangular meshes resulting in polynomial C1-spline functions with affinely uniform shape conditions for the basic functions at the edges, and fitting the 9 value and gradient data at the vertices of the mesh triangles. 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.