Repository: Freie Universität Berlin, Math Department

Polymorphic nodal elements and their application in discontinuous Galerkin methods

Gassner, G.J. and Lörcher, F. and Munz, C.-D. and Hesthaven, J.-S. (2009) Polymorphic nodal elements and their application in discontinuous Galerkin methods. Journal of Computational Physics, 228 (5). 1573-1590 .

Full text not available from this repository.

Official URL:


In this work, we discuss two different but related aspects of the development of efficient discontinuous Galerkin methods on hybrid element grids for the computational modeling of gas dynamics in complex geometries or with adapted grids. In the first part, a recursive construction of different nodal sets for hp finite elements is presented. They share the property that the nodes along the sides of the two-dimensional elements and along the edges of the three-dimensional elements are the Legendre–Gauss–Lobatto points. The different nodal elements are evaluated by computing the Lebesgue constants of the corresponding Vandermonde matrix. In the second part, these nodal elements are applied within the modal discontinuous Galerkin framework. We still use a modal based formulation, but introduce a nodal based integration technique to reduce computational cost in the spirit of pseudospectral methods. We illustrate the performance of the scheme on several large scale applications and discuss its use in a recently developed space-time expansion discontinuous Galerkin scheme.

Item Type:Article
Uncontrolled Keywords:Discontinuous Galerkin; Nodal; Modal; Polynomial interpolation; hp Finite elements; Lebesgue constants; Quadrature free; Unstructured; Triangle; Quadrilateral; Polygonal; Tetrahedron; Hexahedron; Prism; Pentahedron; Pyramid
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:699
Deposited By: Ulrike Eickers
Deposited On:10 Aug 2009 10:28
Last Modified:23 Aug 2009 08:59

Repository Staff Only: item control page