Optimal-order approximation by mixed three-directional spline elements

    Authors

    D. Hong;R. N. Mohapatra

    Abbreviated Journal Title

    Comput. Math. Appl.

    Keywords

    approximation order; B-net representation; bivariate splines; interpolation; triangulation; BIVARIATE PP FUNCTIONS; Computer Science, Interdisciplinary Applications; Mathematics, Applied

    Abstract

    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 [1]), 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.

    Journal Title

    Computers & Mathematics with Applications

    Volume

    40

    Issue/Number

    1

    Publication Date

    1-1-2000

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    127

    Last Page

    135

    WOS Identifier

    WOS:000087294200012

    ISSN

    0898-1221

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