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Triangular finite elements of HCT type and classC ρ

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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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Authors and Affiliations

  1. Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B.P. S 15, Marrakech, Maroc

    M. Laghchim-Lahlou

  2. Laboratoire LANS, INSA, 20, avenue des Buttes de Coësmes, 35043, Rennes, France

    P. Sablonnière

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  1. M. Laghchim-Lahlou
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  2. P. Sablonnière
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Laghchim-Lahlou, M., Sablonnière, P. Triangular finite elements of HCT type and classC ρ . Adv Comput Math 2, 101–122 (1994). https://doi.org/10.1007/BF02519038

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