The flow in a rigid porous medium with a crack is usually modelled by the Darcy equations coupled with the Stokes problem. We first propose a new variational formulation of the Stokes system, where the unknowns are the vorticity, the velocity and the pressure, and describe the corresponding finite-element discretization. We extend this discretization to the case where the Darcy and the Stokes equations are coupled and prove optimal a priori and a posteriori error estimates. We conclude with some numerical experiments.
%0 Journal Article
%1 citeulike:12939631
%A Bernardi, Christine
%A Hecht, Frédéric
%A Nouri, Fatma Z.
%D 2010
%I Oxford University Press
%J IMA Journal of Numerical Analysis
%K 76s05-flows-in-porous-media 76m10-finite-element-methods-in-fluid-mechanics 76d07-stokes-and-related-oseen-etc-flows
%N 1
%P 61--93
%R 10.1093/imanum/drn054
%T A new finite-element discretization of the Stokes problem coupled with the Darcy equations
%U http://dx.doi.org/10.1093/imanum/drn054
%V 30
%X The flow in a rigid porous medium with a crack is usually modelled by the Darcy equations coupled with the Stokes problem. We first propose a new variational formulation of the Stokes system, where the unknowns are the vorticity, the velocity and the pressure, and describe the corresponding finite-element discretization. We extend this discretization to the case where the Darcy and the Stokes equations are coupled and prove optimal a priori and a posteriori error estimates. We conclude with some numerical experiments.
@article{citeulike:12939631,
abstract = {{The flow in a rigid porous medium with a crack is usually modelled by the Darcy equations coupled with the Stokes problem. We first propose a new variational formulation of the Stokes system, where the unknowns are the vorticity, the velocity and the pressure, and describe the corresponding finite-element discretization. We extend this discretization to the case where the Darcy and the Stokes equations are coupled and prove optimal a priori and a posteriori error estimates. We conclude with some numerical experiments.}},
added-at = {2017-06-29T07:13:07.000+0200},
author = {Bernardi, Christine and Hecht, Fr\'{e}d\'{e}ric and Nouri, Fatma Z.},
biburl = {https://www.bibsonomy.org/bibtex/260fe5c7e79d51b3a3a8ccb0abb840194/gdmcbain},
citeulike-article-id = {12939631},
citeulike-linkout-0 = {http://dx.doi.org/10.1093/imanum/drn054},
citeulike-linkout-1 = {http://imajna.oxfordjournals.org/content/30/1/61.abstract},
citeulike-linkout-2 = {http://imajna.oxfordjournals.org/content/30/1/61.full.pdf},
comment = {(private-note)circulated by jon.sauer 2014-01-25},
day = 01,
doi = {10.1093/imanum/drn054},
interhash = {44085d69c5639fc1cd42301c602839a3},
intrahash = {60fe5c7e79d51b3a3a8ccb0abb840194},
issn = {1464-3642},
journal = {IMA Journal of Numerical Analysis},
keywords = {76s05-flows-in-porous-media 76m10-finite-element-methods-in-fluid-mechanics 76d07-stokes-and-related-oseen-etc-flows},
month = jan,
number = 1,
pages = {61--93},
posted-at = {2014-01-27 22:06:53},
priority = {2},
publisher = {Oxford University Press},
timestamp = {2019-02-28T23:44:48.000+0100},
title = {{A new finite-element discretization of the Stokes problem coupled with the Darcy equations}},
url = {http://dx.doi.org/10.1093/imanum/drn054},
volume = 30,
year = 2010
}