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Math."],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We are interested in the discretization of a diffusion problem with highly oscillating coefficient, by a multi-scale finite-element method (MsFEM). The objective of this method is to capture the multi-scale structure of the solution via local basis functions which contain the essential information on small scales. In this paper, we perform an <jats:italic>a posteriori<\/jats:italic> analysis of this discretization. The main result consists of building error indicators with respect to both small and large meshes used in this method. 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