Identifier: 2008-4
Author(s): G.J. Gassner, F. Lorcher, C.-D. Munz and J.S. Hesthaven
Title: Polymorphic Nodal Elements and their Application in Discontinuous Galerkin Methods
Page count: 32 pp.
Abstract:
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 recur- sive construction of different nodal sets for hp finite elements is presented. The different nodal elements are evaluated by computing the Lebesgue constants of the correspond- ing Vandermonde matrix. 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. In the second part, we apply these nodal elements as the basis for discontinuous Galerkin schemes. We shall discuss both the immediate nodal for- mulation as well as the widely used modal formulation where in the latter case a nodal based integration technique is introduced to reduce the computational cost. We shall illus- trate the performance of the scheme on several large scale applications and discuss its use in a recently developed space-time expansion discontinuous Galerkin scheme.
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