From Domain Decomposition to Homogenization Theory
Numerical Analysis
2018-11-16 v1
Abstract
This paper rediscovers a classical homogenization result for a prototypical linear elliptic boundary value problem with periodically oscillating diffusion coefficient. Unlike classical analytical approaches such as asymptotic analysis, oscillating test functions, or two-scale convergence, the result is purely based on the theory of domain decomposition methods and standard finite elements techniques. The arguments naturally generalize to problems far beyond periodicity and scale separation and we provide a brief overview on such applications.
Cite
@article{arxiv.1811.06319,
title = {From Domain Decomposition to Homogenization Theory},
author = {Daniel Peterseim and Dora Varga and Barbara Verfürth},
journal= {arXiv preprint arXiv:1811.06319},
year = {2018}
}
Comments
Submitted for publication in the proceedings of the 25th International Conference on Domain Decomposition Methods