Numerical Method for Elliptic Multiscale Problems

Isabelle Greff and Wolfgang Hackbusch

Contact the author: Please use for correspondence this email.
Submission date: 28. Nov. 2006
Pages: 14
published in: Journal of numerical mathematics, 16 (2008) 2, p. 119-138 
DOI number (of the published article): 10.1515/JNUM.2008.006
Bibtex
MSC-Numbers: 34E13
Keywords and phrases: discrete boundary value problems, multiple scales
Download full preprint: PDF (665 kB), PS ziped (234 kB)

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.