Geodesic
Mortar finite element discretization of a model coupling Darcy and Stokes equations
Bernardi, Christine  ; Rebollo, Tomás Chacón  ; Hecht, Frédéric  ; Mghazli, Zoubida1
1 Équipe d’Ingénierie Mathématique, LIRNE, Faculté des Sciences, Université Ibn Tofail, B.P. 133, Kénitra, Morocco.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 3, pp. 375-410

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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.

DOI : 10.1051/m2an:2008009
Classification : 65N30, 65N55, 76M10
Keywords: Mortar method, finite elements, Darcy equations, Stokes equations

Bernardi, Christine  ; Rebollo, Tomás Chacón  ; Hecht, Frédéric  ; Mghazli, Zoubida 1

1 Équipe d’Ingénierie Mathématique, LIRNE, Faculté des Sciences, Université Ibn Tofail, B.P. 133, Kénitra, Morocco. 
@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 },
     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://geodesic.mathdoc.fr/articles/10.1051/m2an:2008009/}
}
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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 , Tome 42 (2008) no. 3, pp. 375-410. doi: 10.1051/m2an:2008009

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