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Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems

Matthias Maier and Rolf Rannacher

Abstract

This paper introduces an framework for adaptivity for a class of heterogeneous multiscale finite element methods for elliptic problems, which is suitable for a posteriori error estimation with separated quantification of the model error as well as the macroscopic and microscopic discretization errors. The method is derived within a general framework for ‘goal-oriented’ adaptivity, the so-called Dual Weighted Residual (DWR) method. This allows for a systematic a posteriori balancing of multiscale modeling and discretization. The developed method is tested numerically at elliptic diffusion problems for different types of heterogeneous oscillatory coefficients.

MSC 2010: 35J15; 65N12; 65N15; 65N30; 65N50

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Received: 2014-10-28
Revised: 2015-4-15
Accepted: 2015-7-2
Published Online: 2016-10-6
Published in Print: 2016-10-1

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