hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes
We consider the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, new hp-version a prior...
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EDP
2016
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| Online Access: | https://eprints.nottingham.ac.uk/29675/ |
| _version_ | 1848793828814749696 |
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| author | Cangiani, Andrea Dong, Zhaonan Georgoulis, Emmanuil H. Houston, Paul |
| author_facet | Cangiani, Andrea Dong, Zhaonan Georgoulis, Emmanuil H. Houston, Paul |
| author_sort | Cangiani, Andrea |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We consider the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, new hp-version a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/face-degeneration. The proposed method employs elemental polynomial bases of total degree p (P_p-basis) defined in the physical coordinate system, without requiring the mapping from a given reference or canonical frame. Numerical experiments highlighting the performance of the proposed DGFEM are presented. In particular, we study the competitiveness of the p-version DGFEM employing a P_p-basis on both polytopic and tensor-product elements with a (standard) DGFEM employing a (mapped) Q_p-basis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hp-version DGFEM on general agglomerated meshes. |
| first_indexed | 2025-11-14T19:06:30Z |
| format | Article |
| id | nottingham-29675 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:06:30Z |
| publishDate | 2016 |
| publisher | EDP |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-296752020-05-04T17:50:44Z https://eprints.nottingham.ac.uk/29675/ hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes Cangiani, Andrea Dong, Zhaonan Georgoulis, Emmanuil H. Houston, Paul We consider the hp-version interior penalty discontinuous Galerkin finite element method (DGFEM) for the numerical approximation of the advection-diffusion-reaction equation on general computational meshes consisting of polygonal/polyhedral (polytopic) elements. In particular, new hp-version a priori error bounds are derived based on a specific choice of the interior penalty parameter which allows for edge/face-degeneration. The proposed method employs elemental polynomial bases of total degree p (P_p-basis) defined in the physical coordinate system, without requiring the mapping from a given reference or canonical frame. Numerical experiments highlighting the performance of the proposed DGFEM are presented. In particular, we study the competitiveness of the p-version DGFEM employing a P_p-basis on both polytopic and tensor-product elements with a (standard) DGFEM employing a (mapped) Q_p-basis. Moreover, a computational example is also presented which demonstrates the performance of the proposed hp-version DGFEM on general agglomerated meshes. EDP 2016-05-24 Article PeerReviewed Cangiani, Andrea, Dong, Zhaonan, Georgoulis, Emmanuil H. and Houston, Paul (2016) hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes. ESAIM: Mathematical Modelling and Numerical Analysis, 50 (3). pp. 699-725. ISSN 0764-583X discontinuous Galerkin; polygonal elements; polyhedral elements; hp-finite element methods; inverse estimates; P-basis; PDEs with nonnegative characteristic form http://www.esaim-m2an.org/articles/m2an/abs/2016/03/m2an150070/m2an150070.html doi:10.1051/m2an/2015059 doi:10.1051/m2an/2015059 |
| spellingShingle | discontinuous Galerkin; polygonal elements; polyhedral elements; hp-finite element methods; inverse estimates; P-basis; PDEs with nonnegative characteristic form Cangiani, Andrea Dong, Zhaonan Georgoulis, Emmanuil H. Houston, Paul hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes |
| title | hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes |
| title_full | hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes |
| title_fullStr | hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes |
| title_full_unstemmed | hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes |
| title_short | hp-version discontinuous Galerkin methods for advection-diffusion-reaction problems on polytopic meshes |
| title_sort | hp-version discontinuous galerkin methods for advection-diffusion-reaction problems on polytopic meshes |
| topic | discontinuous Galerkin; polygonal elements; polyhedral elements; hp-finite element methods; inverse estimates; P-basis; PDEs with nonnegative characteristic form |
| url | https://eprints.nottingham.ac.uk/29675/ https://eprints.nottingham.ac.uk/29675/ https://eprints.nottingham.ac.uk/29675/ |