A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems
We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) e...
| Main Authors: | , , |
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| Format: | Article |
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2006
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| Online Access: | https://eprints.nottingham.ac.uk/413/ |
| _version_ | 1848790409420996608 |
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| author | Houston, Paul Suli, Endre Wihler, Thomas P. |
| author_facet | Houston, Paul Suli, Endre Wihler, Thomas P. |
| author_sort | Houston, Paul |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments. |
| first_indexed | 2025-11-14T18:12:09Z |
| format | Article |
| id | nottingham-413 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:12:09Z |
| publishDate | 2006 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-4132020-05-04T20:29:59Z https://eprints.nottingham.ac.uk/413/ A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems Houston, Paul Suli, Endre Wihler, Thomas P. We develop the a-posteriori error analysis of hp-version interior-penalty discontinuous Galerkin finite element methods for a class of second-order quasilinear elliptic partial differential equations. Computable upper and lower bounds on the error are derived in terms of a natural (mesh-dependent) energy norm. The bounds are explicit in the local mesh size and the local degree of the approximating polynomial. The performance of the proposed estimators within an automatic hp-adaptive refinement procedure is studied through numerical experiments. 2006 Article NonPeerReviewed Houston, Paul, Suli, Endre and Wihler, Thomas P. (2006) A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems. hp-adaptivity a-posteriori error analysis discontinuous Galerkin finite elemenet methods quasilinear elliptic PDEs |
| spellingShingle | hp-adaptivity a-posteriori error analysis discontinuous Galerkin finite elemenet methods quasilinear elliptic PDEs Houston, Paul Suli, Endre Wihler, Thomas P. A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems |
| title | A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems |
| title_full | A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems |
| title_fullStr | A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems |
| title_full_unstemmed | A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems |
| title_short | A Posteriori Error Analysis of hp-Version Discontinuous Galerkin Finite Element Methods for Second-Order Quasilinear Elliptic Problems |
| title_sort | posteriori error analysis of hp-version discontinuous galerkin finite element methods for second-order quasilinear elliptic problems |
| topic | hp-adaptivity a-posteriori error analysis discontinuous Galerkin finite elemenet methods quasilinear elliptic PDEs |
| url | https://eprints.nottingham.ac.uk/413/ |