On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators
Abstract
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the equation can be incomplete. A theoretical foundation of the approach in the limit of infinitely small oscillations of the coefficients is provided, using the classical theory of homogenization. We present a comprehensive study of the implementation aspects of our method, and a set of numerical tests and comparisons that show the potential practical interest of the approach. The approach detailed in this article improves on an earlier version briefly presented in [C. Le Bris, F. Legoll and K. Li, C. R. Acad. Sci. Paris 2013].
Keywords
Cite
@article{arxiv.1612.05807,
title = {On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators},
author = {Claude Le Bris and Frederic Legoll and Simon Lemaire},
journal= {arXiv preprint arXiv:1612.05807},
year = {2017}
}
Comments
The previous version contained some minor typos, that have now been corrected