A lower bound for the dimension of tetrahedral splines in large degree

DOI10.1007/s00365-023-09625-5arXiv2007.12274OpenAlexW3044430936MaRDI QIDQ6149643

Michael Robert DiPasquale, Nelly Villamizar

Publication date: 5 March 2024

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.12274

zbMATH Keywords

tetrahedral partitionstrivariate spline spacesdimension of spline spaces

Mathematics Subject Classification ID

Spline approximation (41A15) Syzygies, resolutions, complexes and commutative rings (13D02) Computational aspects in algebraic geometry (14Qxx)

Cites Work

• Bounds on the dimension of trivariate spline spaces: a homological approach
• Combinatorial bounds on Hilbert functions of fat points in projective space
• A lower bound for the dimension of trivariate spline spaces
• The algebra of continuous piecewise polynomials
• Bounds on the dimensions of trivariate spline spaces
• Bounds on the dimension of spaces of multivariate piecewise polynomials
• The dimension of bivariate spline spaces of smoothness r for degree \(d\geq 4r+1\)
• Super spline spaces of smoothness \(r\) and degree \(d\geq{} 3r+2\)
• On dimension and existence of local bases for multivariate spline spaces
• Local cohomology of bivariate splines
• A family of ideals of minimal regularity and the Hilbert series of \(C^r(\widehat\Delta)\)
• A spectral sequence for splines
• Algebraic methods in approximation theory
• Polynomial approximation on tetrahedrons in the finite element method
• On the dimension of bivariate spline spaces of smoothness r and degree \(d=3r+1\)
• A dimension series for multivariate splines
• Isogeometric analysis with Bézier tetrahedra
• Isogeometric unstructured tetrahedral and mixed-element Bernstein-Bézier discretizations
• Piecewise polynomials on polyhedral complexes
• Isogeometric triangular Bernstein-Bézier discretizations: automatic mesh generation and geometrically exact finite element analysis
• Spline Functions on Triangulations
• A Nodal Basis for C 1 Piecewise Polynomials of Degree n ≥5
• The Generic Dimension of the Space of $C^1$ Splines of Degree $d \geq 8$ on Tetrahedral Decompositions
• Lectures on Polytopes
• Dimension of mixed splines on polytopal cells
• Isogeometric Analysis
• Piecewise polynomials and the finite element method
• Upper and Lower Bounds on the Dimension of Multivariate Spline Spaces
• Dimension and Local Bases of Homogeneous Spline Spaces
• A Lower Bound for Splines on Tetrahedral Vertex Stars
• Homology of Smooth Splines: Generic Triangulations and a Conjecture of Strang
• Variational methods for the solution of problems of equilibrium and vibrations
• Associated primes of spline complexes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A lower bound for the dimension of tetrahedral splines in large degree