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On the convexity of C 1 surfaces associated with some quadrilateral finite elements

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Abstract

We analyse the convexity property of two classical finite elements and of the associated piecewise polynomial C 1 surfaces. The first one is the piecewise cubic quadrilateral of Fraeijs de Veubeke. The second one is a piecewise quadratic rectangle introduced by Sibson and Thomson and generalized by Sablonnière and Zedek. In both cases, we first study the local problem and then we extend our results to the associated C 1 surfaces.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Granada, Granada, Spain

    J. Lorente‐Pardo & M.C. Serrano‐Pérez

  2. Laboratoire L.A.N.S., I.N.S.A. de Rennes, France

    P. Sablonnière

Authors
  1. J. Lorente‐Pardo
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  2. P. Sablonnière
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  3. M.C. Serrano‐Pérez
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Lorente‐Pardo, J., Sablonnière, P. & Serrano‐Pérez, M. On the convexity of C 1 surfaces associated with some quadrilateral finite elements. Advances in Computational Mathematics 13, 271–292 (2000). https://doi.org/10.1023/A:1018958328042

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  • DOI: https://doi.org/10.1023/A:1018958328042

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