Application of very weak formulation on homogenization of boundary value problems in porous media

Eduard Marušić-Paloka

Czechoslovak Mathematical Journal (2021)

  • Volume: 71, Issue: 4, page 975-989
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Marušić-Paloka, Eduard. "Application of very weak formulation on homogenization of boundary value problems in porous media." Czechoslovak Mathematical Journal 71.4 (2021): 975-989. <http://eudml.org/doc/297472>.

@article{Marušić2021,
abstract = {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.},
author = {Marušić-Paloka, Eduard},
journal = {Czechoslovak Mathematical Journal},
keywords = {homogenization; porous medium; Navier-Stokes system; very weak formulation},
language = {eng},
number = {4},
pages = {975-989},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Application of very weak formulation on homogenization of boundary value problems in porous media},
url = {http://eudml.org/doc/297472},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Marušić-Paloka, Eduard
TI - Application of very weak formulation on homogenization of boundary value problems in porous media
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 4
SP - 975
EP - 989
AB - 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.
LA - eng
KW - homogenization; porous medium; Navier-Stokes system; very weak formulation
UR - http://eudml.org/doc/297472
ER -

References

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