Triangular finite elements of HCT type and classC
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Authors: | M Laghchim-Lahlou P Sablonnière |
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Institution: | 1. Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B.P. S 15, Marrakech, Maroc 2. Laboratoire LANS, INSA, 20, avenue des Buttes de Co?smes, 35043, Rennes, France
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Abstract: | Let τ be some triangulation of a planar polygonal domain Ω. Given a smooth functionu, we construct piecewise polynomial functionsv∈C
ρ(Ω) of degreen=3 ρ for ρ odd, andn=3ρ+1 for ρ even on a subtriangulation τ3 of τ. The latter is obtained by subdividing eachT∈ρ into three triangles, andv/T is a composite triangular finite element, generalizing the classicalC
1 cubic Hsieh-Clough-Tocher (HCT) triangular scheme. The functionv interpolates the derivatives ofu up to order ρ at the vertices of τ. Polynomial degrees obtained in this way are minimal in the family of interpolation schemes
based on finite elements of this type. |
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Keywords: | Triangular finite elements bivariate Hermite interpolation |
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