Multiscale Problems

Multiscale Problems

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The focus of this is on the latest 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 Naviera€“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. Contents:An Introduction to Periodic Homogenization (Alain Damlamian)The Periodic Unfolding Method in Homogenization (Alain Damlamian)Deterministic Homogenization of Stationary Naviera€“Stokes Type Equations (Gabriel Nguetseng a Lazarus Signing)Homogenization of a Class of Imperfect Transmission Problems (Patricia Donato)Decompositions of Displacements of Thin Structures (Georges Griso)Decomposition of Rods Deformations. Asymptotic Behavior of Nonlinear Elastic Rods (Georges Griso)Junction of a Periodic Family of Rods with a Plate in Elasticity (Dominique Blanchard)Multi-scale Modelling of New Composites: Theory and Numerical Simulation (Bernadette Miara)A Priori and a Posteriori Error Analysis for Numerical Homogenization: A Unified Framework (Assyr Abdulle) Readership: PhD students and researchers in applied mathematics, mechanics, physics and engineering. Keywords:Multiscale Problem;Homogenization;Asymptotic Behavior;Approximation... (Y2)]aquot;, (5.20) ii) Wix a€“ W2X, strongly in Lo (Y2), where we have used De Rhama#39;s Theorem to show that the limit of a€“a€“ - - e - VW, is a gradient. ... [T] 5.2 The test functions in Q Set so := \ Homogenization of Imperfect Transmission Problems 131.

Title:Multiscale Problems
Author: Alain Damlamian, Bernadette Miara, Tatsien Li
Publisher:World Scientific - 2011-10-13

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