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We consider the computation of averaged coefficients for the homogenizationof elliptic partial differential equations. In this problem, like in manymultiscale problems, a large number of similar computations parametrized by themacroscopic scale is required at the microscopic scale. This is a frameworkvery much adapted to model order reduction attempts. The purpose of this workis to show how the reduced-basis approach allows to speed up the computation ofa large number of cell problems without any loss of precision. The essentialcomponents of this reduced-basis approach are the {\it a posteriori} errorestimation, which provides sharp error bounds for the outputs of interest, andan approximation process divided into offline and online stages, whichdecouples the generation of the approximation space and its use for Galerkinprojections.

Reduced-Basis Approach for Homogenization beyond the Periodic Setting