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

Morgane Bergot 1 Gary Cohen 1 Marc Durufle 1, 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
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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Morgane Bergot, Gary Cohen, Marc Durufle. Higher-Order Finite Elements for Hybrid Meshes Using New Nodal Pyramidal Elements. Journal of Scientific Computing, Springer Verlag, 2010, 42 (3), pp.345--381. ⟨10.1007/s10915-009-9334-9⟩. ⟨hal-00454261⟩

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