Higher-order discontinuous Galerkin method for pyramidal elements using orthogonal bases



We study finite elements of arbitrarily high-order defined on pyramids for discontinuous Galerkin methods. We propose a new family of high-order pyramidal finite elements using orthogonal basis functions which can be used in hybrid meshes including hexahedra, tetrahedra, wedges, and pyramids. We perform a comparison between these orthogonal functions and nodal functions for affine and non-affine elements. Different strategies for the inversion of the mass matrix are also considered and discussed. Numerical experiments are conducted for the three dimensional Maxwell's equations. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013