  We consider divergence form elliptic operators in dimension $n\geq 2$ with
$L^\infty$ coefficients. Although solutions of these operators are only
H\"{o}lder continuous, we show that they are differentiable ($C^{1,\alpha}$)
with respect to harmonic coordinates. It follows that numerical homogenization
can be extended to situations where the medium has no ergodicity at small
scales and is characterized by a continuum of scales by transferring a new
metric in addition to traditional averaged (homogenized) quantities from
subgrid scales into computational scales and error bounds can be given. This
numerical homogenization method can also be used as a compression tool for
differential operators.
