hp-discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity
In this paper we develop the a posteriori error analysis of the hp-version of the discontinuous Galerkin finite element method for linear and non-linear hyperbolic problems. By employing a duality argument, sharp a posteriori error bounds are derived for certain output functionals of practical inter...
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| Format: | Conference item |
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2002
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| _version_ | 1797072510617911296 |
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| author | Houston, P Senior, B Suli, E |
| author_facet | Houston, P Senior, B Suli, E |
| author_sort | Houston, P |
| collection | OXFORD |
| description | In this paper we develop the a posteriori error analysis of the hp-version of the discontinuous Galerkin finite element method for linear and non-linear hyperbolic problems. By employing a duality argument, sharp a posteriori error bounds are derived for certain output functionals of practical interest. These bounds exhibit an exponential rate of convergence under hp-refinement if either the primal or the dual solution is an analytic function over the computational domain. Based on our a posteriori error bounds, we design and implement the corresponding hp-adaptive finite element algorithm to ensure the reliable and efficient control on the error in the prescribed functional to within a user-defined tolerance. Copyright © 2002 John Wiley and Sons, Ltd. |
| first_indexed | 2024-03-06T23:08:44Z |
| format | Conference item |
| id | oxford-uuid:64bf0bbf-7bb8-4b77-b316-6959663d63df |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:08:44Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:64bf0bbf-7bb8-4b77-b316-6959663d63df2022-03-26T18:20:51Zhp-discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivityConference itemhttp://purl.org/coar/resource_type/c_5794uuid:64bf0bbf-7bb8-4b77-b316-6959663d63dfSymplectic Elements at Oxford2002Houston, PSenior, BSuli, EIn this paper we develop the a posteriori error analysis of the hp-version of the discontinuous Galerkin finite element method for linear and non-linear hyperbolic problems. By employing a duality argument, sharp a posteriori error bounds are derived for certain output functionals of practical interest. These bounds exhibit an exponential rate of convergence under hp-refinement if either the primal or the dual solution is an analytic function over the computational domain. Based on our a posteriori error bounds, we design and implement the corresponding hp-adaptive finite element algorithm to ensure the reliable and efficient control on the error in the prescribed functional to within a user-defined tolerance. Copyright © 2002 John Wiley and Sons, Ltd. |
| spellingShingle | Houston, P Senior, B Suli, E hp-discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity |
| title | hp-discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity |
| title_full | hp-discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity |
| title_fullStr | hp-discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity |
| title_full_unstemmed | hp-discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity |
| title_short | hp-discontinuous Galerkin finite element methods for hyperbolic problems: error analysis and adaptivity |
| title_sort | hp discontinuous galerkin finite element methods for hyperbolic problems error analysis and adaptivity |
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