Homogenization of thermal-hydro-mass transfer processes
Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
February 2015, 8(1): 77-90. doi: 10.3934/dcdss.2015.8.77
Multi-scales H-measures
Luc Tartar 1,
University Professor of Mathematics emeritus, Carnegie Mellon University, Pittsburgh, PA 15213-3890, United States
Received February 2013 Revised July 2013 Published July 2014
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.
Keywords: H-measures, Homogenization, Multi-scale analysis, semi-classical measures..
Mathematics Subject Classification: Primary: 46-xx, 35Sx.
Citation: Luc Tartar. Multi-scales H-measures. Discrete & Continuous Dynamical Systems - S, 2015, 8 (1) : 77-90. doi: 10.3934/dcdss.2015.8.77
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