Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity
A Galerkin finite element method is developed for non–linear, incompressible (hyper) elasticity, and a posteriori error estimates are derived for both linear functionals of the solution and linear functionals of the stress on a boundary where Dirichlet boundary conditions are applied. A second, high...
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| Format: | Journal article |
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2012
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| _version_ | 1826295910663979008 |
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| author | Whiteley, J Tavener, S |
| author_facet | Whiteley, J Tavener, S |
| author_sort | Whiteley, J |
| collection | OXFORD |
| description | A Galerkin finite element method is developed for non–linear, incompressible (hyper) elasticity, and a posteriori error estimates are derived for both linear functionals of the solution and linear functionals of the stress on a boundary where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution demonstrates the accuracy of the error estimators. Finally the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity. |
| first_indexed | 2024-03-07T04:08:14Z |
| format | Journal article |
| id | oxford-uuid:c6f0d5c2-fc81-42c6-bb75-435d0fc231da |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:08:14Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:c6f0d5c2-fc81-42c6-bb75-435d0fc231da2022-03-27T06:41:27ZError estimation and adaptivity for incompressible, non–linear (hyper–)elasticityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c6f0d5c2-fc81-42c6-bb75-435d0fc231daMathematical Institute - ePrints2012Whiteley, JTavener, SA Galerkin finite element method is developed for non–linear, incompressible (hyper) elasticity, and a posteriori error estimates are derived for both linear functionals of the solution and linear functionals of the stress on a boundary where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution demonstrates the accuracy of the error estimators. Finally the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity. |
| spellingShingle | Whiteley, J Tavener, S Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity |
| title | Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity |
| title_full | Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity |
| title_fullStr | Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity |
| title_full_unstemmed | Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity |
| title_short | Error estimation and adaptivity for incompressible, non–linear (hyper–)elasticity |
| title_sort | error estimation and adaptivity for incompressible non linear hyper elasticity |
| work_keys_str_mv | AT whiteleyj errorestimationandadaptivityforincompressiblenonlinearhyperelasticity AT taveners errorestimationandadaptivityforincompressiblenonlinearhyperelasticity |