hp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems
We consider the a posteriori error analysis of hp-discontinuous Galerkin finite element approximations to first--order hyperbolic problems. In particular, we discuss the question of error estimation for linear functionals, such as the outflow flux and the local average of the solution. Based on our...
| Main Authors: | , |
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| Format: | Report |
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Unspecified
2001
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| _version_ | 1797085969248157696 |
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| author | Houston, P Suli, E |
| author_facet | Houston, P Suli, E |
| author_sort | Houston, P |
| collection | OXFORD |
| description | We consider the a posteriori error analysis of hp-discontinuous Galerkin finite element approximations to first--order hyperbolic problems. In particular, we discuss the question of error estimation for linear functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local polynomial-degree-variation and local mesh subdivision. The theoretical results are illustrated by a series of numerical experiments. |
| first_indexed | 2024-03-07T02:15:19Z |
| format | Report |
| id | oxford-uuid:a207b8d0-c746-4a57-879c-f0101bed5df0 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:15:19Z |
| publishDate | 2001 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:a207b8d0-c746-4a57-879c-f0101bed5df02022-03-27T02:17:23Zhp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problemsReporthttp://purl.org/coar/resource_type/c_93fcuuid:a207b8d0-c746-4a57-879c-f0101bed5df0Mathematical Institute - ePrintsUnspecified2001Houston, PSuli, EWe consider the a posteriori error analysis of hp-discontinuous Galerkin finite element approximations to first--order hyperbolic problems. In particular, we discuss the question of error estimation for linear functionals, such as the outflow flux and the local average of the solution. Based on our a posteriori error bound we design and implement the corresponding adaptive algorithm to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local polynomial-degree-variation and local mesh subdivision. The theoretical results are illustrated by a series of numerical experiments. |
| spellingShingle | Houston, P Suli, E hp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title | hp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title_full | hp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title_fullStr | hp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title_full_unstemmed | hp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title_short | hp-Adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems |
| title_sort | hp adaptive discontinuous galerkin finite element methods for first order hyperbolic problems |
| work_keys_str_mv | AT houstonp hpadaptivediscontinuousgalerkinfiniteelementmethodsforfirstorderhyperbolicproblems AT sulie hpadaptivediscontinuousgalerkinfiniteelementmethodsforfirstorderhyperbolicproblems |