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This paper presents two new approaches for finding the homogenizedcoefficients of multiscale elliptic PDEs. Standard approaches for computing thehomogenized coefficients suffer from the so-called resonance error, originatingfrom a mismatch between the true and the computational boundary conditions. Ournew methods, based on solutions of parabolic and elliptic cell-problems, resultin an exponential decay of the resonance error.

Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems