Extraction and application of super-smooth cubic B-splines over triangulations
Abstract
The space of cubic Clough-Tocher splines is a classical finite element approximation space over triangulations for solving partial differential equations. However, for such a space there is no B-spline basis available, which is a preferred choice in computer aided geometric design and isogeometric analysis. A B-spline basis is a locally supported basis that forms a convex partition of unity. In this paper, we explore several alternative cubic spline spaces over triangulations equipped with a B-spline basis. They are defined over a Powell-Sabin refined triangulation and present different types of super-smoothness. The super-smooth B-splines are obtained through an extraction process, i.e., they are expressed in terms of less smooth basis functions. These alternative spline spaces maintain the same optimal approximation power as Clough-Tocher splines. This is illustrated with a selection of numerical examples in the context of least squares approximation and finite element approximation for second and fourth order boundary value problems.
Keywords
Cite
@article{arxiv.2305.02057,
title = {Extraction and application of super-smooth cubic B-splines over triangulations},
author = {Jan Grošelj and Hendrik Speleers},
journal= {arXiv preprint arXiv:2305.02057},
year = {2023}
}