Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem
This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the inter...
| Main Authors: | , , , , |
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| Format: | Article |
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Global Science
2010
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| Online Access: | https://eprints.nottingham.ac.uk/1099/ |
| _version_ | 1848790538969415680 |
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| author | Cliffe, Andrew Hall, Edward Houston, Paul Phipps, Eric T. Salinger, Andrew G. |
| author_facet | Cliffe, Andrew Hall, Edward Houston, Paul Phipps, Eric T. Salinger, Andrew G. |
| author_sort | Cliffe, Andrew |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method. A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual (DWR) approach. Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator. |
| first_indexed | 2025-11-14T18:14:13Z |
| format | Article |
| id | nottingham-1099 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:14:13Z |
| publishDate | 2010 |
| publisher | Global Science |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-10992020-05-04T20:24:49Z https://eprints.nottingham.ac.uk/1099/ Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem Cliffe, Andrew Hall, Edward Houston, Paul Phipps, Eric T. Salinger, Andrew G. This article is concerned with the numerical detection of bifurcation points of nonlinear partial differential equations as some parameter of interest is varied. In particular, we study in detail the numerical approximation of the Bratu problem, based on exploiting the symmetric version of the interior penalty discontinuous Galerkin finite element method. A framework for a posteriori control of the discretization error in the computed critical parameter value is developed based upon the application of the dual weighted residual (DWR) approach. Numerical experiments are presented to highlight the practical performance of the proposed a posteriori error estimator. Global Science 2010-10 Article NonPeerReviewed Cliffe, Andrew, Hall, Edward, Houston, Paul, Phipps, Eric T. and Salinger, Andrew G. (2010) Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem. Communications in Computational Physics, 8 (4). pp. 845-865. ISSN 1815-2406 (Submitted) http://www.global-sci.com/freedownload/v8_845.pdf doi:10.4208/cicp.290709.120210a doi:10.4208/cicp.290709.120210a |
| spellingShingle | Cliffe, Andrew Hall, Edward Houston, Paul Phipps, Eric T. Salinger, Andrew G. Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem |
| title | Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem |
| title_full | Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem |
| title_fullStr | Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem |
| title_full_unstemmed | Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem |
| title_short | Adaptivity and a posteriori error control for bifurcation problems I: the Bratu problem |
| title_sort | adaptivity and a posteriori error control for bifurcation problems i: the bratu problem |
| url | https://eprints.nottingham.ac.uk/1099/ https://eprints.nottingham.ac.uk/1099/ https://eprints.nottingham.ac.uk/1099/ |