Polymorphic nodal elements and their application in discontinuous Galerkin methods
| Autor: | Gregor J. Gassner, Frieder Lörcher, Claus-Dieter Munz, Jan S. Hesthaven |
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| Rok vydání: | 2009 |
| Předmět: |
Mathematical optimization
Physics and Astronomy (miscellaneous) Lebesgue constants Tetrahedron Nodal Unstructured hp Finite elements Lebesgue integration symbols.namesake Polynomial interpolation Discontinuous Galerkin method Discontinuous Galerkin Applied mathematics Hexahedron Mathematics Triangle Numerical Analysis Quadrilateral Applied Mathematics Pentahedron Vandermonde matrix Finite element method Polygonal Computer Science Applications Computational Mathematics Prism Pyramid Modeling and Simulation Quadrature free symbols Modal |
| Zdroj: | Journal of Computational Physics. 228:1573-1590 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2008.11.012 |
| Popis: | 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. (c) 2008 Elsevier Inc. All rights reserved. |
| Databáze: | OpenAIRE |
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