A new finite element of \(C^ 1\) cubic splines (Q1196871)
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scientific article; zbMATH DE number 89621
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A new finite element of \(C^ 1\) cubic splines |
scientific article; zbMATH DE number 89621 |
Statements
A new finite element of \(C^ 1\) cubic splines (English)
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16 January 1993
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Many authors developed a special method to consider the spline interpolation element on micro-triangulations. The Clough-Tocher splitting and the Powell-Sabin splitting are the most used examples. In the present paper, a new finite element with dimension 16 of \(C^ 1\) cubic splines which have interpolation schemes on the Morgan-Scott triangulation is given. A basic theorem points out that the considered interpolation problem is solvable and unique. The proof of the theorem needs the Bernstein-Bézier representation of bivariate splines.
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\(C^ 1\) cubic splines
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spline interpolation
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micro-triangulations
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Clough-Tocher splitting
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Powell-Sabin splitting
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Morgan-Scott triangulation
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Bernstein-Bézier representation
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bivariate splines
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