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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Optimal-Order Approximation by Mixed Three-Directional Spline Elements

Hong, Don, Mohapatra, R. N. 16 May 2000 (has links)
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.

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