Multi-scales H-measures

Luc Tartar

doi:10.3934/dcdss.2015.8.77

Article Contents

2015, Volume 8, Issue 1: 77-90. Doi: 10.3934/dcdss.2015.8.77

This issue Previous Article Homogenization of thermal-hydro-mass transfer processes Next Article Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Multi-scales H-measures

Luc Tartar^1,

1.
University Professor of Mathematics emeritus, Carnegie Mellon University, Pittsburgh, PA 15213-3890

Received: February 2013

Revised: July 2013

Published: February 2015

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Abstract

This paper introduces a new tool so called Multi-scales H-measures to analyse the effect of heterogeneities occurring at several scales. In a first place, it recalls the course that brought the introduction of new tools for homogenization and it recalls what are H-Measures. Then the paper gives the definition and the framework of Semi-Classical Measures, presents their capability, and illustrates some of their limitations. Finally, it introduces the concept of Multi-Scale H-measures.

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Mathematics Subject Classification: Primary: 46-xx, 35Sxx.

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References

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