We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
138/2006
Numerical Method for Elliptic Multiscale Problems
Isabelle Greff and Wolfgang Hackbusch
Abstract
In this paper we are interested in the coarse-mesh approximations of a class of second order elliptic operators with rough or rapidly oscillatory coefficients. We intend to provide a smoother elliptic operator which on a coarse mesh behaves like the original operator. Note that there is no requirement on smoothness or periodicity of the coefficients. To simplify the theory and the numerical implementations, we restrict ourselves to the one-dimensional case.
