A symmetric counterexample to Strang's conjecture for bivariate $C^1$ cubic splines on triangulations
Year: 2026
Type: preprint
Abstract: We exhibit a triangulation of an equilateral triangle for which the space of bivariate $C^1$ cubic splines has dimension larger than the dimension formula conjectured by Strang. Notably, the triangulation is such that no two edges sharing a vertex are collinear, and the triangulation is invariant under the action of the isometry group ($D_3$) of the equilateral triangle which is triangulated.
Source: arXiv (Cornell University)
Author: Potu, Pratyush
Institution: Brown University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220954070