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Higher‐order discontinuous Galerkin method for pyramidal elements using orthogonal bases
Author(s) -
Bergot Morgane,
Duruflé Marc
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21703
Subject(s) - affine transformation , tetrahedron , polygon mesh , discontinuous galerkin method , finite element method , hexahedron , mathematics , basis function , galerkin method , partial differential equation , mathematical analysis , pure mathematics , geometry , physics , thermodynamics
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