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We develop a multiscale tailored finite point method (MsTFPM) for second order elliptic equations with rough or highly oscillatory coefficients. The finite point method has been tailored to some particular properties of the problem, so that it can capture the multiscale solutions using coarse meshes without resolving the fine scale structure of the solution. Several numerical examples in one-and two-dimensions are provided to show the accuracy and convergence of the proposed method. Indoi:10.4310/cms.2012.v10.n3.a11 fatcat:cpewngzwv5bshbe54bp5b2u2pq