A high-order corrector estimate for a semi-linear elliptic system in perforated domains

We derive in this Note a high-order corrector estimate for the homogenization of a microscopic semi-linear elliptic system posed in perforated domains. The major challenges are the presence of nonlinear volume and surface reaction rates. This type of correctors justifies mathematically the convergence rate of formal asymptotic expansions for the two-scale homogenization settings. As the main tool, we use energy-like estimates to investigate the error estimate between the micro and macro concentrations and between the corresponding micro- and macro-concentration gradients. This work aims at generalizing the results reported in [1,2].