Adaptive energy minimisation for hp-finite element methods
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in an adaptive manner. Specifically, we outline a new approach...
| Main Authors: | , |
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| Format: | Article |
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Elsevier
2016
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| Online Access: | https://eprints.nottingham.ac.uk/29676/ |
| _version_ | 1848793829115691008 |
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| author | Houston, Paul Wihler, Thomas P. |
| author_facet | Houston, Paul Wihler, Thomas P. |
| author_sort | Houston, Paul |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in an adaptive manner. Specifically, we outline a new approach in the context of hp-adaptive finite element methods employed for the efficient numerical solution of linear and nonlinear second-order boundary value problems. Numerical experiments are presented which highlight the practical performance of this new hp-refinement technique for both one- and two-dimensional problems. |
| first_indexed | 2025-11-14T19:06:31Z |
| format | Article |
| id | nottingham-29676 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:06:31Z |
| publishDate | 2016 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-296762020-05-04T17:37:25Z https://eprints.nottingham.ac.uk/29676/ Adaptive energy minimisation for hp-finite element methods Houston, Paul Wihler, Thomas P. This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in an adaptive manner. Specifically, we outline a new approach in the context of hp-adaptive finite element methods employed for the efficient numerical solution of linear and nonlinear second-order boundary value problems. Numerical experiments are presented which highlight the practical performance of this new hp-refinement technique for both one- and two-dimensional problems. Elsevier 2016-02-10 Article PeerReviewed Houston, Paul and Wihler, Thomas P. (2016) Adaptive energy minimisation for hp-finite element methods. Computers and Mathematics with Applications, 71 (4). pp. 977-990. ISSN 0898-1221 http://www.sciencedirect.com/science/article/pii/S0898122116000055 doi:10.1016/j.camwa.2016.01.002 doi:10.1016/j.camwa.2016.01.002 |
| spellingShingle | Houston, Paul Wihler, Thomas P. Adaptive energy minimisation for hp-finite element methods |
| title | Adaptive energy minimisation for hp-finite element methods |
| title_full | Adaptive energy minimisation for hp-finite element methods |
| title_fullStr | Adaptive energy minimisation for hp-finite element methods |
| title_full_unstemmed | Adaptive energy minimisation for hp-finite element methods |
| title_short | Adaptive energy minimisation for hp-finite element methods |
| title_sort | adaptive energy minimisation for hp-finite element methods |
| url | https://eprints.nottingham.ac.uk/29676/ https://eprints.nottingham.ac.uk/29676/ https://eprints.nottingham.ac.uk/29676/ |