Sharp convergence rates for the homogenization of the Stokes equations in a perforated domain

This paper addresses the homogenization of the Stokes equations in a periodic perforated domain. The homogenized model is known to correspond to Darcy's law in the full domain. We established a sharp convergence rate O(√ε) for the energy norm of the difference in velocities, where ε represents the size of the solid obstacles. This was achieved by using a two-scale asymptotic expansion of the Stokes equations and a new construction of a cut-off function that avoids the introduction of boundary layers. The main novelty is that our analysis applies to the physically relevant case of a porous medium where each fluid and solid part is a connected subdomain.