hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes

Cangiani, Andrea and Georgoulis, Emmanuil H. and Houston, Paul (2014) hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes. Mathematical Models and Methods in Applied Sciences, 24 (10). pp. 2009-2041. ISSN 0218-2025

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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 analysed. Utilizing a bounding box concept, the method employs elemental polynomial bases of total degree p (P_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_p-basis in comparison to the conforming p-version finite element method on tensor-product elements is studied numerically for a simple test problem.

Item Type: Article
Additional Information: Electronic version of an article published in Mathematical Models and Methods, vol. 24, issue 10, 2014, p. 2009-2041, doi: 10.1142/S0218202514500146 ©World Scientific Publishing Company http://www.worldscientific.com/worldscinet/m3as
Keywords: Discontinuous Galerkin, polygonal elements, polyhedral elements, hp-finite elements, inverse estimates, P-basis
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1142/S0218202514500146
Depositing User: Houston, Paul
Date Deposited: 26 Aug 2015 14:19
Last Modified: 14 Sep 2016 16:56
URI: http://eprints.nottingham.ac.uk/id/eprint/29669

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