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Multiscale techniques for parabolic equations
We use the local orthogonal decomposition technique introduced in Målqvist and Peterseim (Math Comput 83(290):2583–2603, 2014) to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale coefficients. We consider nonsmooth initial data and a ba...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2017
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5762871/ https://www.ncbi.nlm.nih.gov/pubmed/29375160 http://dx.doi.org/10.1007/s00211-017-0905-7 |
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author | Målqvist, Axel Persson, Anna |
author_facet | Målqvist, Axel Persson, Anna |
author_sort | Målqvist, Axel |
collection | PubMed |
description | We use the local orthogonal decomposition technique introduced in Målqvist and Peterseim (Math Comput 83(290):2583–2603, 2014) to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale coefficients. We consider nonsmooth initial data and a backward Euler scheme for the temporal discretization. Optimal order convergence rate, depending only on the contrast, but not on the variations of the coefficients, is proven in the [Formula: see text] -norm. We present numerical examples, which confirm our theoretical findings. |
format | Online Article Text |
id | pubmed-5762871 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-57628712018-01-25 Multiscale techniques for parabolic equations Målqvist, Axel Persson, Anna Numer Math (Heidelb) Article We use the local orthogonal decomposition technique introduced in Målqvist and Peterseim (Math Comput 83(290):2583–2603, 2014) to derive a generalized finite element method for linear and semilinear parabolic equations with spatial multiscale coefficients. We consider nonsmooth initial data and a backward Euler scheme for the temporal discretization. Optimal order convergence rate, depending only on the contrast, but not on the variations of the coefficients, is proven in the [Formula: see text] -norm. We present numerical examples, which confirm our theoretical findings. Springer Berlin Heidelberg 2017-07-20 2018 /pmc/articles/PMC5762871/ /pubmed/29375160 http://dx.doi.org/10.1007/s00211-017-0905-7 Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Article Målqvist, Axel Persson, Anna Multiscale techniques for parabolic equations |
title | Multiscale techniques for parabolic equations |
title_full | Multiscale techniques for parabolic equations |
title_fullStr | Multiscale techniques for parabolic equations |
title_full_unstemmed | Multiscale techniques for parabolic equations |
title_short | Multiscale techniques for parabolic equations |
title_sort | multiscale techniques for parabolic equations |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5762871/ https://www.ncbi.nlm.nih.gov/pubmed/29375160 http://dx.doi.org/10.1007/s00211-017-0905-7 |
work_keys_str_mv | AT malqvistaxel multiscaletechniquesforparabolicequations AT perssonanna multiscaletechniquesforparabolicequations |