Title

Optimal-Order Approximation By Mixed Three-Directional Spline Elements

Keywords

Approximation order; B-net representation; Bivariate splines; Interpolation; Triangulation

Abstract

This paper is concerned with a study of approximation order and construction of locally supported elements for the space S41 (Δ) of Cl quartic pp (piecewise polynomial) functions on a triangulation Δ of a connected polygonal domain Ω in R2. It is well known that, when Δ is a three-directional mesh Δ(1), the order of approximation of S41(Δ(1)) is only 4, not 5. Though a local Clough-Tocher refinement procedure of an arbitrary triangulation A yields the optimal (fifth) order of approximation from the space S41(Δ) (see [1]), it needs more data points in addition to the vertex set of the triangulation A. In this paper, we will introduce a particular mixed three-directional mesh Δ(3)) and construct so-called mixed three-directional elements. We prove that the space S41(Δ(3)) achieves its optimal-order of approximation by constructing an interpolation scheme using mixed three-directional elements. © 2000 Elsevier Science Ltd. All rights reserved.

Publication Date

5-16-2000

Publication Title

Computers and Mathematics with Applications

Volume

40

Issue

1

Number of Pages

127-135

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0898-1221(00)00146-2

Socpus ID

0034230825 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0034230825

This document is currently not available here.

Share

COinS