MATHICSE-GroupAbdulle, AssyrArjmand, DoghonayPaganoni, Edoardo2019-03-292019-03-292019-03-292019-03-3010.5075/epfl-MATHICSE-265009https://infoscience.epfl.ch/handle/20.500.14299/155801This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a mismatch between the true and the computational boundary conditions. Our new methods, based on solutions of parabolic and elliptic cell-problems, result in an exponential decay of the resonance error.text::working paper