The focus of this is on the lgest developments related to the analysis of problems in which several scales are presented.After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier-Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials)and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated.

Preface

Alain Damlamian

An Introduction to Periodic Homogenization

Alain Damlamian

The Periodic Unfolding Method in Homogenization

Gabriel Nguetseng and Lazarus Signing

Deterministic Homogenization of Stationary Navier-Stokes

Type Equations

Patricia Donato

Homogenization of a Class of Imperfect Transmission Problems

Georges Griso

Decompositions of Displacements of Thin Structures

Georges Griso

Decomposition of Rods Deformations. Asymptotic Behavior of

Nonlinear Elastic Rods

Dominique Blanchard

Junction of a Periodic Family of Rods with a Plate

in Elasticity

Bernadette Miara

Multi-scale Modelling of New Composites: Theory and

Numerical Simulation

Assyr Abdulle

A Priori and a Posteriori Error Analysis for Numerical

Homogenization: A Unified Framework