A goal oriented error estimator and mesh adaptivity for sea ice simulations
For the first time we introduce an error estimator for the numerical approximation of the equations describing the dynamics of sea ice. The idea of the estimator is to identify different error contributions coming from spatial and temporal discretization as well as from the splitting in time of the...
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Online Access: | https://dx.doi.org/10.48550/arxiv.2002.04350 https://arxiv.org/abs/2002.04350 |
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ftdatacite:10.48550/arxiv.2002.04350 2023-05-15T18:17:20+02:00 A goal oriented error estimator and mesh adaptivity for sea ice simulations Mehlmann, Carolin Richter, Thomas 2020 https://dx.doi.org/10.48550/arxiv.2002.04350 https://arxiv.org/abs/2002.04350 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Numerical Analysis math.NA FOS Mathematics Article CreativeWork article Preprint 2020 ftdatacite https://doi.org/10.48550/arxiv.2002.04350 2022-03-10T16:04:11Z For the first time we introduce an error estimator for the numerical approximation of the equations describing the dynamics of sea ice. The idea of the estimator is to identify different error contributions coming from spatial and temporal discretization as well as from the splitting in time of the ice momentum equations from further parts of the coupled system. The novelty of the error estimator lies in the consideration of the splitting error, which turns out to be dominant with increasing mesh resolution. Errors are measured in user specified functional outputs like the total sea ice extent. The error estimator is based on the dual weighted residual method that asks for the solution of an additional dual problem for obtaining sensitivity information. Estimated errors can be used to validate the accuracy of the solution and, more relevant, to reduce the discretization error by guiding an adaptive algorithm that optimally balances the mesh size and the time step size to increase the efficiency of the simulation. Article in Journal/Newspaper Sea ice DataCite Metadata Store (German National Library of Science and Technology) |
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Open Polar |
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DataCite Metadata Store (German National Library of Science and Technology) |
op_collection_id |
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language |
unknown |
topic |
Numerical Analysis math.NA FOS Mathematics |
spellingShingle |
Numerical Analysis math.NA FOS Mathematics Mehlmann, Carolin Richter, Thomas A goal oriented error estimator and mesh adaptivity for sea ice simulations |
topic_facet |
Numerical Analysis math.NA FOS Mathematics |
description |
For the first time we introduce an error estimator for the numerical approximation of the equations describing the dynamics of sea ice. The idea of the estimator is to identify different error contributions coming from spatial and temporal discretization as well as from the splitting in time of the ice momentum equations from further parts of the coupled system. The novelty of the error estimator lies in the consideration of the splitting error, which turns out to be dominant with increasing mesh resolution. Errors are measured in user specified functional outputs like the total sea ice extent. The error estimator is based on the dual weighted residual method that asks for the solution of an additional dual problem for obtaining sensitivity information. Estimated errors can be used to validate the accuracy of the solution and, more relevant, to reduce the discretization error by guiding an adaptive algorithm that optimally balances the mesh size and the time step size to increase the efficiency of the simulation. |
format |
Article in Journal/Newspaper |
author |
Mehlmann, Carolin Richter, Thomas |
author_facet |
Mehlmann, Carolin Richter, Thomas |
author_sort |
Mehlmann, Carolin |
title |
A goal oriented error estimator and mesh adaptivity for sea ice simulations |
title_short |
A goal oriented error estimator and mesh adaptivity for sea ice simulations |
title_full |
A goal oriented error estimator and mesh adaptivity for sea ice simulations |
title_fullStr |
A goal oriented error estimator and mesh adaptivity for sea ice simulations |
title_full_unstemmed |
A goal oriented error estimator and mesh adaptivity for sea ice simulations |
title_sort |
goal oriented error estimator and mesh adaptivity for sea ice simulations |
publisher |
arXiv |
publishDate |
2020 |
url |
https://dx.doi.org/10.48550/arxiv.2002.04350 https://arxiv.org/abs/2002.04350 |
genre |
Sea ice |
genre_facet |
Sea ice |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.2002.04350 |
_version_ |
1766191475829243904 |