Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems
We revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the so called...
| Main Authors: | , , |
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| Format: | Conference Paper |
| Published: |
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/48945 |
| _version_ | 1848758129486987264 |
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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 revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the so called optimal test space norm by using an element subgrid discretization. This should make the DPG method not only stable but also robust, that is, uniformly stable with respect to the P'eclet number in the current application. The effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation. © 2011 Published by Elsevier Ltd. |
| first_indexed | 2025-11-14T09:39:05Z |
| format | Conference Paper |
| id | curtin-20.500.11937-48945 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:39:05Z |
| publishDate | 2011 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-489452017-09-13T15:41:42Z Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems Niemi, A. Collier, N. Calo, Victor We revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the so called optimal test space norm by using an element subgrid discretization. This should make the DPG method not only stable but also robust, that is, uniformly stable with respect to the P'eclet number in the current application. The effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation. © 2011 Published by Elsevier Ltd. 2011 Conference Paper http://hdl.handle.net/20.500.11937/48945 10.1016/j.procs.2011.04.202 http://creativecommons.org/licenses/by-nc-nd/3.0/ fulltext |
| spellingShingle | Niemi, A. Collier, N. Calo, Victor Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems |
| title | Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems |
| title_full | Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems |
| title_fullStr | Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems |
| title_full_unstemmed | Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems |
| title_short | Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems |
| title_sort | discontinuous petrov-galerkin method based on the optimal test space norm for one-dimensional transport problems |
| url | http://hdl.handle.net/20.500.11937/48945 |