An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems
We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy...
| Main Authors: | , , |
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| Format: | Article |
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Oxford University Press
2008
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| Online Access: | https://eprints.nottingham.ac.uk/913/ |
| _version_ | 1848790501106384896 |
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| author | Georgoulis, Emmanuil H. Houston, Paul Virtanen, Juha |
| author_facet | Georgoulis, Emmanuil H. Houston, Paul Virtanen, Juha |
| author_sort | Georgoulis, Emmanuil H. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems. |
| first_indexed | 2025-11-14T18:13:37Z |
| format | Article |
| id | nottingham-913 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:13:37Z |
| publishDate | 2008 |
| publisher | Oxford University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-9132020-05-04T20:27:44Z https://eprints.nottingham.ac.uk/913/ An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems Georgoulis, Emmanuil H. Houston, Paul Virtanen, Juha We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems. Oxford University Press 2008 Article NonPeerReviewed Georgoulis, Emmanuil H., Houston, Paul and Virtanen, Juha (2008) An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems. IMA Journal of Numerical Analysis . (Submitted) |
| spellingShingle | Georgoulis, Emmanuil H. Houston, Paul Virtanen, Juha An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems |
| title | An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems |
| title_full | An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems |
| title_fullStr | An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems |
| title_full_unstemmed | An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems |
| title_short | An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems |
| title_sort | a posteriori error indicator for discontinuous galerkin approximations of fourth order elliptic problems |
| url | https://eprints.nottingham.ac.uk/913/ |