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.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-2-1597 |
| Date | 16 May 2000 |
| Creators | Hong, Don, Mohapatra, R. N. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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