Partial homogenization of discrete models

Abstract

This article is devoted to the approximation of discrete models by semi-discrete (and semi-continuous) models. The partial homogenization method is applied to this end. The interface conditions between the discrete part and the continuous part are discussed. The error estimates for the solutions of discrete and semi-discrete models are proved.

Keywords:

• semi-discrete models
• partial asymptotic domain decomposition
• strongly oscillating coefficients
• finite element method
• quasicontinuum method

AMS Subject Classifications: :

• 35B27
• 35Q53
• 35C20

Acknowledgements

The work was done during the stay of M. Bétoué Etoughé in the Laboratory of Mathematics of the University of Saint Etienne (LaMUSE). The authors were supported by regional Rhône-Alpes grant 04-022487-01 ‘Multi-scale modelling of nano-structures’ and by the PPF multidisciplinary grant ALLIANA.