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Preprints, Working Papers, ... Year : 2024

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.
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Dates and versions

hal-04541828 , version 1 (11-04-2024)
hal-04541828 , version 2 (07-05-2024)

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  • HAL Id : hal-04541828 , version 2

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Loïc Balazi, Grégoire Allaire, Pascal Omnes. Sharp convergence rates for the homogenization of the Stokes equations in a perforated domain. 2024. ⟨hal-04541828v2⟩
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