Sharp convergence rates for the homogenization of the Stokes equations in a perforated domain
Abstract
This paper is concerned with the homogenization of the Stokes equations in a periodic perforated domain. The homogenized model is known to be Darcy's law in the full domain. We establish a sharp convergence rate $O(\sqrt{\varepsilon})$ for the energy norm of the difference of the velocities, where $\varepsilon$ represents the size of the solid obstacles. This is achieved by using a two-scale asymptotic expansion of the Stokes equations and a new construction of a cut-off function which avoids the introduction of boundary layers. The main novelty is that our analysis applies for the physically relevant case of a porous medium where each of the fluid and solid parts is a connected subdomain.
Domains
Mathematics [math]
Origin : Files produced by the author(s)
Licence : CC BY - Attribution
Licence : CC BY - Attribution