Publications

2013

• Higher-Order Discontinuous Galerkin Method for Pyramidal Elements using Orthogonal Bases
  
  • Bergot Morgane
  • Duruflé Marc
  Numerical Methods for Partial Differential Equations, Wiley, 2013, 29 (1), pp.144-169. 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. (10.1002/num.21703)
  DOI : 10.1002/num.21703