Construction of Local Quartic Spline Elements for Optimal-Order Approximation |
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Authors: | Charles K Chui Dong Hong |
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Institution: | Center for Approximation Theory, Texas A&M University, College Station, Texas 77843 ; Center for Approximation Theory, Texas A&M University, College Station, Texas 77843 |
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Abstract: | This paper is concerned with a study of approximation order and construction of locally supported elements for the space of (piecewise polynomial) functions on an arbitrary triangulation of a connected polygonal domain in . It is well known that even when is a three-directional mesh , the order of approximation of is only 4, not 5. The objective of this paper is two-fold: (i) A local Clough-Tocher refinement procedure of an arbitrary triangulation is introduced so as to yield the optimal (fifth) order of approximation, where locality means that only a few isolated triangles need refinement, and (ii) locally supported Hermite elements are constructed to achieve the optimal order of approximation. |
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Keywords: | Approximation order B-net representations bivariate splines local Clough-Tocher refinement star-vertex splines triangulations |
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