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In this paper, we formulate an adaptive two\u2010grid numerical finite element discretization of the double\u2010diffusion system and perform a comparison between the micro\u2010 and macro\u2010model. Our numerical results show that the micro\u2010model solutions appear to converge to the macro\u2010model linearly with the parameter <jats:italic>\u03b5<\/jats:italic> of periodic geometry. 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