hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes
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...
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| Format: | Article |
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World Scientific
2014
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| Online Access: | https://eprints.nottingham.ac.uk/29669/ |
| _version_ | 1848793826707111936 |
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| author | Cangiani, Andrea Georgoulis, Emmanuil H. Houston, Paul |
| author_facet | Cangiani, Andrea Georgoulis, Emmanuil H. Houston, Paul |
| author_sort | Cangiani, Andrea |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:06:28Z |
| format | Article |
| id | nottingham-29669 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:06:28Z |
| publishDate | 2014 |
| publisher | World Scientific |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-296692020-05-04T16:44:58Z https://eprints.nottingham.ac.uk/29669/ hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes Cangiani, Andrea Georgoulis, Emmanuil H. Houston, Paul 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. World Scientific 2014-03-11 Article PeerReviewed Cangiani, Andrea, 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 Discontinuous Galerkin polygonal elements polyhedral elements hp-finite elements inverse estimates P-basis http://www.worldscientific.com/doi/abs/10.1142/S0218202514500146 doi:10.1142/S0218202514500146 doi:10.1142/S0218202514500146 |
| spellingShingle | Discontinuous Galerkin polygonal elements polyhedral elements hp-finite elements inverse estimates P-basis Cangiani, Andrea Georgoulis, Emmanuil H. Houston, Paul hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title | hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title_full | hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title_fullStr | hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title_full_unstemmed | hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title_short | hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes |
| title_sort | hp-version discontinuous galerkin methods on polygonal and polyhedral meshes |
| topic | Discontinuous Galerkin polygonal elements polyhedral elements hp-finite elements inverse estimates P-basis |
| url | https://eprints.nottingham.ac.uk/29669/ https://eprints.nottingham.ac.uk/29669/ https://eprints.nottingham.ac.uk/29669/ |