Geodesic
Application of very weak formulation on homogenization of boundary value problems in porous media
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 975-989.

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The goal of this paper is to present a different approach to the homogenization of the Dirichlet boundary value problem in porous medium. Unlike the standard energy method or the method of two-scale convergence, this approach is not based on the weak formulation of the problem but on the very weak formulation. To illustrate the method and its advantages we treat the stationary, incompressible Navier-Stokes system with the non-homogeneous Dirichlet boundary condition in periodic porous medium. The nonzero velocity trace on the boundary of a solid inclusion yields a non-standard addition to the source term in the Darcy law. In addition, the homogenized model is not incompressible.
DOI : 10.21136/CMJ.2021.0161-20
Classification : 35B27, 35Q30, 76M50
Keywords: homogenization; porous medium; Navier-Stokes system; very weak formulation 
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     title = {Application of very weak formulation on homogenization of boundary value problems in porous media},
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Marušić-Paloka, Eduard. Application of very weak formulation on homogenization of boundary value problems in porous media. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 975-989. doi : 10.21136/CMJ.2021.0161-20. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0161-20/

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