Finite element methods for hyperbolic problems: a posteriori error analysis and adaptivity
This paper presents an overview of recent developments in the area of a posteriori error estimation for first-order hyperbolic partial differential equations. Global a posteriori error bounds are derived in the $H^{-1}$ norm for steady and unsteady finite element and finite volume approximations of...
| Main Authors: | , |
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| Format: | Report |
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Unspecified
1996
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| _version_ | 1797056893361848320 |
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| author | Suli, E Houston, P |
| author_facet | Suli, E Houston, P |
| author_sort | Suli, E |
| collection | OXFORD |
| description | This paper presents an overview of recent developments in the area of a posteriori error estimation for first-order hyperbolic partial differential equations. Global a posteriori error bounds are derived in the $H^{-1}$ norm for steady and unsteady finite element and finite volume approximations of hyperbolic systems and scalar hyperbolic equations. We also consider the problem of a posteriori error estimation for linear functionals of the solution. The a posteriori error bounds are implemented into an adaptive finite element algorithm. |
| first_indexed | 2024-03-06T19:28:54Z |
| format | Report |
| id | oxford-uuid:1cc3f640-dac4-4a66-88ba-ea785a2196b3 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:28:54Z |
| publishDate | 1996 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:1cc3f640-dac4-4a66-88ba-ea785a2196b32022-03-26T11:07:17ZFinite element methods for hyperbolic problems: a posteriori error analysis and adaptivityReporthttp://purl.org/coar/resource_type/c_93fcuuid:1cc3f640-dac4-4a66-88ba-ea785a2196b3Mathematical Institute - ePrintsUnspecified1996Suli, EHouston, PThis paper presents an overview of recent developments in the area of a posteriori error estimation for first-order hyperbolic partial differential equations. Global a posteriori error bounds are derived in the $H^{-1}$ norm for steady and unsteady finite element and finite volume approximations of hyperbolic systems and scalar hyperbolic equations. We also consider the problem of a posteriori error estimation for linear functionals of the solution. The a posteriori error bounds are implemented into an adaptive finite element algorithm. |
| spellingShingle | Suli, E Houston, P Finite element methods for hyperbolic problems: a posteriori error analysis and adaptivity |
| title | Finite element methods for hyperbolic problems: a posteriori error analysis and adaptivity |
| title_full | Finite element methods for hyperbolic problems: a posteriori error analysis and adaptivity |
| title_fullStr | Finite element methods for hyperbolic problems: a posteriori error analysis and adaptivity |
| title_full_unstemmed | Finite element methods for hyperbolic problems: a posteriori error analysis and adaptivity |
| title_short | Finite element methods for hyperbolic problems: a posteriori error analysis and adaptivity |
| title_sort | finite element methods for hyperbolic problems a posteriori error analysis and adaptivity |
| work_keys_str_mv | AT sulie finiteelementmethodsforhyperbolicproblemsaposteriorierroranalysisandadaptivity AT houstonp finiteelementmethodsforhyperbolicproblemsaposteriorierroranalysisandadaptivity |