  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.
