Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems
Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni · Comptes Rendus Mathématique · 2019
This 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.