Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions
We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors me...
| Main Authors: | , , , |
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| Format: | Article |
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World Scientific
2009
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| Online Access: | https://eprints.nottingham.ac.uk/1140/ |
| _version_ | 1848790542800912384 |
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| author | Zhu, Liang Giani, Stefano Houston, Paul Schoetzau, Dominik |
| author_facet | Zhu, Liang Giani, Stefano Houston, Paul Schoetzau, Dominik |
| author_sort | Zhu, Liang |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities. |
| first_indexed | 2025-11-14T18:14:17Z |
| format | Article |
| id | nottingham-1140 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:14:17Z |
| publishDate | 2009 |
| publisher | World Scientific |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-11402020-05-04T20:27:08Z https://eprints.nottingham.ac.uk/1140/ Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions Zhu, Liang Giani, Stefano Houston, Paul Schoetzau, Dominik We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities. World Scientific 2009 Article NonPeerReviewed Zhu, Liang, Giani, Stefano, Houston, Paul and Schoetzau, Dominik (2009) Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions. Mathematical Models and Methods in Applied Sciences (M3AS) . ISSN 0218-2025 (Submitted) http://www.worldscinet.com/m3as/m3as.shtml |
| spellingShingle | Zhu, Liang Giani, Stefano Houston, Paul Schoetzau, Dominik Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions |
| title | Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions |
| title_full | Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions |
| title_fullStr | Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions |
| title_full_unstemmed | Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions |
| title_short | Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions |
| title_sort | energy norm a-posteriori error estimation for hp-adaptive discontinuous galerkin methods for elliptic problems in three dimensions |
| url | https://eprints.nottingham.ac.uk/1140/ https://eprints.nottingham.ac.uk/1140/ |