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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...

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Detalles Bibliográficos
Autores principales: Målqvist, Axel, Persson, Anna
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2017
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.
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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
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