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

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. Key words: pyramidal element, higher-order finite element, hybrid mesh, conformal mesh, continuous finite element, discontinuous Galerkin method, error estimates, quadrature for-mula