The Department of Mathematical Sciences

University of Bath

**Abstract**: A problem of homogenization of a divergence type
second order uniformly elliptic operator is considered with arbitrary bounded
rapidly oscillating periodic coefficients, either with periodic
.outer. boundary conditions or in the whole space. It is proved that if the
right-hand side is Gevrey regular (in particular analytic) then by optimally
truncating the full two-scale asymptotic expansion for the solution one obtains
an approximation with an exponentially small error. The optimality of the
exponential error bound is established for a one-dimensional example by proving
the analogous lower bound.