An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems
In this paper we present a residual-based {\em a posteriori} error estimator for $hp$-adaptive discontinuous Galerkin (DG) methods for elliptic eigenvalue problems. In particular we use as a model problem the Laplace eigenvalue problem on bounded domains in $\mathbb{R}^d$, $d=2,3$, with homogeneous...
| Main Authors: | , |
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| Format: | Article |
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World Scientific
2011
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| Online Access: | https://eprints.nottingham.ac.uk/1498/ |
| _version_ | 1848790617696501760 |
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| author | Giani, Stefano Hall, Edward |
| author_facet | Giani, Stefano Hall, Edward |
| author_sort | Giani, Stefano |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this paper we present a residual-based {\em a posteriori} error estimator for $hp$-adaptive discontinuous Galerkin (DG) methods for elliptic eigenvalue problems. In particular we use as a model problem the Laplace eigenvalue problem on bounded domains in $\mathbb{R}^d$, $d=2,3$, with homogeneous Dirichlet boundary conditions. Analogous error estimators can be easily obtained for more complicated elliptic eigenvalue problems.
We prove the reliability and efficiency of the residual based error estimator and use numerical experiments to show that, under an $hp$-adaptation strategy driven by the error estimator, exponential convergence can be achieved, even for non--smooth eigenfunctions. |
| first_indexed | 2025-11-14T18:15:28Z |
| format | Article |
| id | nottingham-1498 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:15:28Z |
| publishDate | 2011 |
| publisher | World Scientific |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-14982020-05-04T20:23:53Z https://eprints.nottingham.ac.uk/1498/ An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems Giani, Stefano Hall, Edward In this paper we present a residual-based {\em a posteriori} error estimator for $hp$-adaptive discontinuous Galerkin (DG) methods for elliptic eigenvalue problems. In particular we use as a model problem the Laplace eigenvalue problem on bounded domains in $\mathbb{R}^d$, $d=2,3$, with homogeneous Dirichlet boundary conditions. Analogous error estimators can be easily obtained for more complicated elliptic eigenvalue problems. We prove the reliability and efficiency of the residual based error estimator and use numerical experiments to show that, under an $hp$-adaptation strategy driven by the error estimator, exponential convergence can be achieved, even for non--smooth eigenfunctions. World Scientific 2011 Article NonPeerReviewed Giani, Stefano and Hall, Edward (2011) An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems. Mathematical Models and Methods in Applied Sciences (M3AS), 22 (10). p. 1299001. ISSN 0218-2025 (Submitted) http://www.worldscinet.com/m3as/m3as.shtml |
| spellingShingle | Giani, Stefano Hall, Edward An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems |
| title | An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems |
| title_full | An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems |
| title_fullStr | An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems |
| title_full_unstemmed | An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems |
| title_short | An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems |
| title_sort | a posteriori error estimator for hp-adaptive discontinuous galerkin methods for elliptic eigenvalue problems |
| url | https://eprints.nottingham.ac.uk/1498/ https://eprints.nottingham.ac.uk/1498/ |