Homogenization in polygonal domains
David Gérard‐Varet, Nader Masmoudi · Journal of the European Mathematical Society · 2011
We consider the homogenization of elliptic systems with \varepsilon -periodic coefficients. Classical two-scale approximation yields a O(\varepsilon) error inside the domain. We discuss here the existence of higher order corrections, in the case of general polygonal domains. The corrector depends in a non-trivial way on the boundary. Our analysis extends substantially previous results obtained for polygonal domains with sides of rational slopes.