Bivariate C2 cubic spline quasi-interpolants on uniform Powell---Sabin triangulations of a rectangular domain

Authors:
Sara Remogna
Affiliations:
Department of Mathematics, University of Torino, Torino, Italy 10 --- 10123
Venue:
Advances in Computational Mathematics
Year:
2012

Citing 7
Cited 0

Bernstein--Bézier representation and near-minimally normed discrete quasi-interpolation operators

Applied Numerical Mathematics
Approximating partial derivatives of first and second order by quadratic spline quasi-interpolants on uniform meshes

Mathematics and Computers in Simulation
Matrix-valued subdivision schemes for generating surfaces with extraordinary vertices

Computer Aided Geometric Design
On near-best discrete quasi-interpolation on a four-directional mesh

Journal of Computational and Applied Mathematics
Near-best quasi-interpolants associated with H-splines on a three-direction mesh

Journal of Computational and Applied Mathematics
C2 piecewise cubic quasi-interpolants on a 6-direction mesh

Journal of Approximation Theory
Constructing good coefficient functionals for bivariate C1 quadratic spline quasi-interpolants

MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we construct discrete quasi-interpolants based on C 2 cubic multi-box splines on uniform Powell---Sabin triangulations of a rectangular domain. The main problem consists in finding the coefficient functionals associated with boundary multi-box splines (i.e. multi-box splines whose supports overlap with the domain) involving data points inside or on the boundary of the domain and giving the optimal approximation order. They are obtained either by minimizing an upper bound for the infinity norm of the operator w.r.t. a finite number of free parameters, or by inducing the superconvergence of the gradient of the quasi-interpolant at some specific points of the domain. Finally, we give norm and error estimates and we provide some numerical examples illustrating the approximation properties of the proposed operators.