Higher-Order Discontinuous Galerkin Method for Pyramidal Elements using Orthogonal Bases

Morgane Bergot (1) , Marc Duruflé (2, 3)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 IMB - Institut de Mathématiques de Bordeaux
3 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems

We study arbitrarily high-order finite elements defined on pyramids on discontinuous Galerkin methods. We propose a new family of high-order pyramidal finite element 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 mass matrix are also considered and discussed. Numerical experiments are conducted for 3-D Maxwell's equations.

Mots clés: Pyramidal element; Higher-order finite element; Hybrid mesh; Conformal mesh; Discontinuous Galerkin method; Orthogonal basis functions

Domaines: Equations aux dérivées partielles [math.AP]

Morgane Bergot, Marc Duruflé. Higher-Order Discontinuous Galerkin Method for Pyramidal Elements using Orthogonal Bases. Numerical Methods for Partial Differential Equations, 2013, 29 (1), pp.144-169. ⟨10.1002/num.21703⟩. ⟨hal-00547319v2⟩