Optimal-order approximation by mixed three-directional spline elements
Abbreviated Journal Title
Comput. Math. Appl.
approximation order; B-net representation; bivariate splines; interpolation; triangulation; BIVARIATE PP FUNCTIONS; Computer Science, Interdisciplinary Applications; Mathematics, Applied
This paper is concerned with a study of approximation order and construction of locally supported elements for the space S-4(1)(Delta) of C-1 quartic pp (piecewise polynomial) functions on a triangulation Delta of a connected polygonal domain Omega in R-2. It is well known that, when Delta is a three-directional mesh Delta((1)), the order of approximation of S-4(1)(Delta((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 S-4(1)(Delta) (see ), it needs more data points in addition to the vertex set of the triangulation Delta. In this paper, we will introduce a particular mixed three-directional mesh Delta((3)) and construct so-called mixed three-directional elements. We prove that the space S-4(1)(Delta((3))) achieves its optimal-order of approximation by constructing an interpolation scheme using mixed three-directional elements. (C) 2000 Elsevier Science Ltd. All rights reserved.
Computers & Mathematics with Applications
Article; Proceedings Paper
"Optimal-order approximation by mixed three-directional spline elements" (2000). Faculty Bibliography 2000s. 2612.