A \(C^r\) trivariate macro-element based on the Alfeld split of tetrahedra (Q741100)
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scientific article; zbMATH DE number 6342400
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A \(C^r\) trivariate macro-element based on the Alfeld split of tetrahedra |
scientific article; zbMATH DE number 6342400 |
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A \(C^r\) trivariate macro-element based on the Alfeld split of tetrahedra (English)
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10 September 2014
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After a review of the smoothness conditions for two trivariate polynomials that share a common triangular face and the minimal degree conditions for bivariate macro-elements on the Clough-Tocher split of a triangle and on non-split triangles, the authors derive minimal degree conditions for the macro-elements over the Alfeld split of a tetrahedron. The main results of this paper are the derivation of a local and stable minimal determining set for macro-elements on one tetrahedron and a collection of tetrahedra as well as the corresponding dimension formulae. Several examples round up the paper.
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trivariate splines
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\(C^r\) smoothness
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macro-elements
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Alfeld refinement
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