Numerical approximation of the fluctuations in random heterogeneous problems

In this talk, we consider random heterogeneous problems. Inspired by the recents works of F. Otto, M. Duerinckx and A. Gloria, our aim is to understand how much the response fluctuates around its homogenized limit. In other words, we wish to estimate the distribution of the response, on the basis of the knowledge of the distribution of the material coefficients, and without resorting to a costly Monte Carlo approach. In the first part of the talk, we show that, in a weakly random setting, the fluctuations of the response are governed by a tensor that we identify. In the second part of the talk, we consider strongly random settings, and we present numerical simulations that confirm our theoretical findings.

Joint work with F. Legoll (ENPC).