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hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes

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posted on 2014-06-02, 12:47 authored by Andrea Cangiani, Emmanuil H. Georgoulis, Paul Houston
An hp-version interior penalty discontinuous Galerkin method (DGFEM) for the numerical solution of second-order elliptic partial differential equations on general computational meshes consisting of polygonal/polyhedral elements is presented and analyzed. Utilizing a bounding box concept, the method employs elemental polynomial bases of total degree p (P[subscript p]-basis) defined on the physical space, without the need to map from a given reference or canonical frame. This, together with a new specific choice of the interior penalty parameter which allows for face-degeneration, ensures that optimal a priori bounds may be established, for general meshes including polygonal elements with degenerating edges in two dimensions and polyhedral elements with degenerating faces and/or edges in three dimensions. Numerical experiments highlighting the performance of the proposed method are presented. Moreover, the competitiveness of the p-version DGFEM employing a P[subscript p]-basis in comparison to the conforming p-version finite element method on tensor-product elements is studied numerically for a simple test problem.

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Citation

Mathematical Models and Methods in Applied Sciences, 2014, 24 (10) pp. 2009-2041

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • AM (Accepted Manuscript)

Published in

Mathematical Models and Methods in Applied Sciences

Publisher

World Scientific Publishing

issn

0218-2025

eissn

1793-6314

Copyright date

2014

Available date

2015-03-12

Publisher version

http://www.worldscientific.com/doi/abs/10.1142/S0218202514500146

Notes

Electronic version of an article published as Mathematical Models and Methods in Applied Sciences, 24 (10), 2014, DOI:10.1142/S0218202514500146 © copyright World Scientific Publishing Company http://www.worldscientific.com/doi/abs/10.1142/S0218202514500146

Language

en

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