Higher‐order discontinuous Galerkin method for pyramidal elements using orthogonal bases |
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Authors: | Morgane Bergot Marc Duruflé |
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Affiliation: | 1. Projet POems, INRIA Rocquencourt, Le Chesnay, France;2. Institut Mathématique de Bordeaux, Université Bordeaux I, Bordeaux, France |
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Abstract: | 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 |
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Keywords: | conformal mesh discontinuous Galerkin method higher‐order finite element hybrid mesh orthogonal basis functions pyramidal element |
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