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Multiscale techniques for parabolic equations

Journal article
Authors Axel Målqvist
Anna Persson
Published in Numerische Mathematik
Volume 138
Issue 1
Pages 191-217
ISSN 0029-599X
Publication year 2018
Published at Department of Mathematical Sciences
Pages 191-217
Language en
Links doi.org/10.1007/s00211-017-0905-7
https://gup.ub.gu.se/file/207299
Keywords finite-element methods, spaces, Mathematics
Subject categories Applied mathematics

Abstract

We use the local orthogonal decomposition technique introduced in MAlqvist 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 -norm. We present numerical examples, which confirm our theoretical findings.

Page Manager: Webmaster|Last update: 9/11/2012
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