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Multiscale techniques for parabolic equations

By Axel M\ue5lqvist and Anna Persson

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

Topics: Applied Mechanics, Computational Mathematics, Mathematical Analysis
Publisher: 'Springer Science and Business Media LLC'
Year: 2018
DOI identifier: 10.1007/s00211-017-0905-7
OAI identifier: oai:research.chalmers.se:500565
Provided by: Chalmers Research

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