C2 piecewise cubic quasi-interpolants on a 6-direction mesh

Davydov, O. and Sablonnière, P. (2010) C2 piecewise cubic quasi-interpolants on a 6-direction mesh. Journal of Approximation Theory, 162 (3). pp. 528-544. ISSN 0021-9045 (https://doi.org/10.1016/j.jat.2009.09.006)

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Abstract

We study two kinds of quasi-interpolants (abbr. QI) in the space of C2 piecewise cubics in the plane, or in a rectangular domain, endowed with the highly symmetric triangulation generated by a uniform 6-direction mesh. It has been proved recently that this space is generated by the integer translates of two multi-box splines. One kind of QIs is of differential type and the other of discrete type. As those QIs are exact on the space of cubic polynomials, their approximation order is 4 for sufficiently smooth functions. In addition, they exhibit nice superconvergent properties at some specific points. Moreover, the infinite norms of the discrete QIs being small, they give excellent approximations of a smooth function and of its first order partial derivatives. The approximation properties of the QIs are illustrated by numerical examples.

  • Item type:Article
    ID code:20210
    Dates:
    Date
    Event
    31 March 2010
    Published
    2 October 2009
    Published Online
    25 September 2009
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Mrs Carolynne Westwood
    Date deposited:09 Jun 2010 11:49
    Last modified:08 Apr 2024 18:36
    URI:https://strathprints.strath.ac.uk/id/eprint/20210
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