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.
@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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {42},
year = {2008},
pages = {375-410},
doi = {10.1051/m2an:2008009},
mrnumber = {2423791},
zbl = {1138.76044},
language = {en},
url = {http://dml.mathdoc.fr/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 42 (2008) pp. 375-410. doi : 10.1051/m2an:2008009. http://gdmltest.u-ga.fr/item/M2AN_2008__42_3_375_0/
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