Explicit-in-time goal-oriented adaptivity
Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of interest as an integral over the whole space–time domain. A full space–time va...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Published: |
Elsevier BV
2019
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| Online Access: | http://hdl.handle.net/20.500.11937/74550 |
| _version_ | 1848763306618126336 |
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| author | Muñoz-Matute, J. Calo, Victor Pardo, D. Alberdi, E. van der Zee, K. |
| author_facet | Muñoz-Matute, J. Calo, Victor Pardo, D. Alberdi, E. van der Zee, K. |
| author_sort | Muñoz-Matute, J. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of interest as an integral over the whole space–time domain. A full space–time variational formulation allows such representation. Most authors employ implicit time marching schemes to perform goal-oriented adaptivity as it is known that they can be reinterpreted as Galerkin methods. In this work, we consider variational forms for explicit methods in time. We derive an appropriate error representation and propose a goal-oriented adaptive algorithm in space. For that, we derive the forward Euler method in time employing a discontinuous-in-time Petrov–Galerkin formulation. In terms of time domain adaptivity, we impose the Courant–Friedrichs–Lewy condition to ensure the stability of the method. We provide some numerical results in 1D space + time for the diffusion and advection–diffusion equations to show the performance of the proposed explicit-in-time goal-oriented adaptive algorithm. |
| first_indexed | 2025-11-14T11:01:22Z |
| format | Journal Article |
| id | curtin-20.500.11937-74550 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:01:22Z |
| publishDate | 2019 |
| publisher | Elsevier BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-745502021-01-06T03:42:51Z Explicit-in-time goal-oriented adaptivity Muñoz-Matute, J. Calo, Victor Pardo, D. Alberdi, E. van der Zee, K. Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of interest as an integral over the whole space–time domain. A full space–time variational formulation allows such representation. Most authors employ implicit time marching schemes to perform goal-oriented adaptivity as it is known that they can be reinterpreted as Galerkin methods. In this work, we consider variational forms for explicit methods in time. We derive an appropriate error representation and propose a goal-oriented adaptive algorithm in space. For that, we derive the forward Euler method in time employing a discontinuous-in-time Petrov–Galerkin formulation. In terms of time domain adaptivity, we impose the Courant–Friedrichs–Lewy condition to ensure the stability of the method. We provide some numerical results in 1D space + time for the diffusion and advection–diffusion equations to show the performance of the proposed explicit-in-time goal-oriented adaptive algorithm. 2019 Journal Article http://hdl.handle.net/20.500.11937/74550 10.1016/j.cma.2018.12.028 http://creativecommons.org/licenses/by-nc-nd/4.0/ Elsevier BV fulltext |
| spellingShingle | Muñoz-Matute, J. Calo, Victor Pardo, D. Alberdi, E. van der Zee, K. Explicit-in-time goal-oriented adaptivity |
| title | Explicit-in-time goal-oriented adaptivity |
| title_full | Explicit-in-time goal-oriented adaptivity |
| title_fullStr | Explicit-in-time goal-oriented adaptivity |
| title_full_unstemmed | Explicit-in-time goal-oriented adaptivity |
| title_short | Explicit-in-time goal-oriented adaptivity |
| title_sort | explicit-in-time goal-oriented adaptivity |
| url | http://hdl.handle.net/20.500.11937/74550 |