A representation and comparison of three cubic macro-elements

Ema Češek, Jan Grošelj, Andrej Kolar-Požun, Maruša Lekše, Gašper Domen Romih, Ada Šadl Praprotnik and Matija Šteblaj

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 219, issue C, 527-543

Abstract: The paper is concerned with three types of cubic splines over a triangulation that are characterized by three degrees of freedom associated with each vertex of the triangulation. The splines differ in computational complexity, polynomial reproduction properties, and smoothness. With the aim to make them a versatile tool for numerical analysis, a unified representation in terms of locally supported basis functions is established. The construction of these functions is based on geometric concepts and is expressed in the Bernstein–Bézier form. They are readily applicable in a range of standard approximation methods, which is demonstrated by a number of numerical experiments.

Keywords: Splines over triangulations; Bernstein–Bézier techniques; Macro-elements; Spline basis; Spline approximation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:219:y:2024:i:c:p:527-543

DOI: 10.1016/j.matcom.2023.12.042

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