An abstract analysis of optimal goal-oriented adaptivity
We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of (Carstensen, Feischl, Page, and Praetorius, Axioms of adaptivity, Comput. Math. Appl., 67 (2014), pp. 1195–1253). We prove that this framework covers standar...
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| Format: | Article |
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Society for Industrial and Applied Mathematics
2016
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| Online Access: | https://eprints.nottingham.ac.uk/32679/ |
| _version_ | 1848794465729249280 |
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| author | Feischl, Michael Praetorius, Dirk van der Zee, Kristoffer George |
| author_facet | Feischl, Michael Praetorius, Dirk van der Zee, Kristoffer George |
| author_sort | Feischl, Michael |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of (Carstensen, Feischl, Page, and Praetorius, Axioms of adaptivity, Comput. Math. Appl., 67 (2014), pp. 1195–1253). We prove that this framework covers standard discretizations of general second-order linear elliptic PDEs and hence generalizes available results beyond the Poisson equation. |
| first_indexed | 2025-11-14T19:16:38Z |
| format | Article |
| id | nottingham-32679 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:16:38Z |
| publishDate | 2016 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-326792020-05-04T17:52:04Z https://eprints.nottingham.ac.uk/32679/ An abstract analysis of optimal goal-oriented adaptivity Feischl, Michael Praetorius, Dirk van der Zee, Kristoffer George We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of (Carstensen, Feischl, Page, and Praetorius, Axioms of adaptivity, Comput. Math. Appl., 67 (2014), pp. 1195–1253). We prove that this framework covers standard discretizations of general second-order linear elliptic PDEs and hence generalizes available results beyond the Poisson equation. Society for Industrial and Applied Mathematics 2016-05-12 Article PeerReviewed Feischl, Michael, Praetorius, Dirk and van der Zee, Kristoffer George (2016) An abstract analysis of optimal goal-oriented adaptivity. SIAM Journal on Numerical Analysis, 54 (3). pp. 1423-1448. ISSN 1095-7170 Adaptivity goal-oriented algorithm quantity of interest convergence optimal convergence rates finite element method boundary element method http://epubs.siam.org/doi/abs/10.1137/15M1021982 doi:10.1137/15M1021982 doi:10.1137/15M1021982 |
| spellingShingle | Adaptivity goal-oriented algorithm quantity of interest convergence optimal convergence rates finite element method boundary element method Feischl, Michael Praetorius, Dirk van der Zee, Kristoffer George An abstract analysis of optimal goal-oriented adaptivity |
| title | An abstract analysis of optimal goal-oriented adaptivity |
| title_full | An abstract analysis of optimal goal-oriented adaptivity |
| title_fullStr | An abstract analysis of optimal goal-oriented adaptivity |
| title_full_unstemmed | An abstract analysis of optimal goal-oriented adaptivity |
| title_short | An abstract analysis of optimal goal-oriented adaptivity |
| title_sort | abstract analysis of optimal goal-oriented adaptivity |
| topic | Adaptivity goal-oriented algorithm quantity of interest convergence optimal convergence rates finite element method boundary element method |
| url | https://eprints.nottingham.ac.uk/32679/ https://eprints.nottingham.ac.uk/32679/ https://eprints.nottingham.ac.uk/32679/ |