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Higher-order Finite Elements for Hybrid Meshes Using New Nodal Pyramidal Elements

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Abstract

We provide a comprehensive study of arbitrarily high-order finite elements defined on pyramids. We propose a new family of high-order nodal pyramidal finite element which can be used in hybrid meshes which include hexahedra, tetrahedra, wedges and pyramids. Finite elements matrices can be evaluated through approximate integration, and we show that the order of convergence of the method is conserved. Numerical results demonstrate the efficiency of hybrid meshes compared to pure tetrahedral meshes or hexahedral meshes obtained by splitting tetrahedra into hexahedra.

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Authors and Affiliations

  1. Projet POems, INRIA Rocquencourt, Le Chesnay, France

    Morgane Bergot & Gary Cohen

  2. Institut Mathématique de Bordeaux, Université Bordeaux I, Bordeaux, France

    Marc Duruflé

Authors
  1. Morgane Bergot
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  2. Gary Cohen
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  3. Marc Duruflé
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Correspondence to Morgane Bergot.

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Bergot, M., Cohen, G. & Duruflé, M. Higher-order Finite Elements for Hybrid Meshes Using New Nodal Pyramidal Elements. J Sci Comput 42, 345–381 (2010). https://doi.org/10.1007/s10915-009-9334-9

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  • DOI: https://doi.org/10.1007/s10915-009-9334-9

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