Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm
We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numeri...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Pergamon Press
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/51474 |
| _version_ | 1848758706982879232 |
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| author | Niemi, A. Collier, N. Calo, Victor |
| author_facet | Niemi, A. Collier, N. Calo, Victor |
| author_sort | Niemi, A. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view. © 2013 Elsevier Ltd. All rights reserved. |
| first_indexed | 2025-11-14T09:48:16Z |
| format | Journal Article |
| id | curtin-20.500.11937-51474 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:48:16Z |
| publishDate | 2013 |
| publisher | Pergamon Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-514742018-03-29T09:08:25Z Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm Niemi, A. Collier, N. Calo, Victor We investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm improves the robustness of the DPG method with respect to vanishing diffusion. We numerically compare coarse-mesh accuracy of the approximation when using the quasi-optimal norm, the standard norm, and the weighted norm. Our results show that the quasi-optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions. We address the problems associated to the resolution of the optimal test functions with respect to the quasi-optimal norm by studying their convergence numerically. In order to facilitate understanding of the method, we also include a detailed explanation of the methodology from the algorithmic point of view. © 2013 Elsevier Ltd. All rights reserved. 2013 Journal Article http://hdl.handle.net/20.500.11937/51474 10.1016/j.camwa.2013.07.016 Pergamon Press restricted |
| spellingShingle | Niemi, A. Collier, N. Calo, Victor Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm |
| title | Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm |
| title_full | Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm |
| title_fullStr | Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm |
| title_full_unstemmed | Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm |
| title_short | Automatically stable discontinuous Petrov-Galerkin methods for stationary transport problems: Quasi-optimal test space norm |
| title_sort | automatically stable discontinuous petrov-galerkin methods for stationary transport problems: quasi-optimal test space norm |
| url | http://hdl.handle.net/20.500.11937/51474 |