As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where the Darcy and Stokes equations are coupled via appropriate matching conditions on the interface. We propose a discretization of this problem which combines the mortar method with standard finite elements, in order to handle separately the flow inside and outside the porous medium. We prove a priori and a posteriori error estimates for the resulting discrete problem. Some numerical experiments confirm the interest of the discretization.
Mots clés : Mortar method, finite elements, Darcy equations, Stokes equations
@article{M2AN_2008__42_3_375_0,
author = {Bernardi, Christine and Rebollo, Tom\'as Chac\'on and Hecht, Fr\'ed\'eric and Mghazli, Zoubida},
title = {Mortar finite element discretization of a model coupling {Darcy} and {Stokes} equations},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {375--410},
publisher = {EDP-Sciences},
volume = {42},
number = {3},
year = {2008},
doi = {10.1051/m2an:2008009},
mrnumber = {2423791},
zbl = {1138.76044},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2008009/}
}
TY - JOUR AU - Bernardi, Christine AU - Rebollo, Tomás Chacón AU - Hecht, Frédéric AU - Mghazli, Zoubida TI - Mortar finite element discretization of a model coupling Darcy and Stokes equations JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 375 EP - 410 VL - 42 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2008009/ DO - 10.1051/m2an:2008009 LA - en ID - M2AN_2008__42_3_375_0 ER -
%0 Journal Article %A Bernardi, Christine %A Rebollo, Tomás Chacón %A Hecht, Frédéric %A Mghazli, Zoubida %T Mortar finite element discretization of a model coupling Darcy and Stokes equations %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 375-410 %V 42 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2008009/ %R 10.1051/m2an:2008009 %G en %F M2AN_2008__42_3_375_0
Bernardi, Christine; Rebollo, Tomás Chacón; Hecht, Frédéric; Mghazli, Zoubida. Mortar finite element discretization of a model coupling Darcy and Stokes equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 3, pp. 375-410. doi : 10.1051/m2an:2008009. http://archive.numdam.org/articles/10.1051/m2an:2008009/
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