Section: New Results

Numerical homogenization

Inspired by the quantitative analysis of [17] and [48] , Z. Habibi (former SIMPAF post-doctoral fellow) and A. Gloria introduced in [14] a general method to reduce the so-called resonance error in numerical homogenization, both at the levels of the approximation of the homogenized coefficients and of the correctors. This method significantly extends [2] . The method relies on the introduction of a massive term in the corrector equation and of a systematic use of Richardson extrapolation. In the three academic examples of heterogeneous coefficients (periodic, quasiperiodic, and Poisson random inclusions), the method yields optimal theoretical and empirical convergence rates, and outperforms most of the other existing methods.