On two-scale convergence

Authors:
Luděk Nechvátal
Affiliations:
Department of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic
Venue:
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Year:
2003

Citing 4
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Two-scale limits in some non-linear problems of engineering mechanics

Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics

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Abstract

Two-scale convergence is a special weak convergence used in homogenization theory. Besides the original definitions by Nguetseng and Allaire, the paper introduces an alternative approach based on Arbogast's idea of two-scale transform which changes a sequence of one-variable functions into a sequence of two-variable functions. Although it leads to the same convergence, it simplifies some proofs.