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

Mortar finite element discretization of a model coupling Darcy and Stokes equations. (English) Zbl 1138.76044

ESAIM, Math. Model. Numer. Anal. 42, No. 3, 375-410 (2008).
Summary: As a first draft of a model for a river flowing on a homogeneous porous ground, we consider a system where 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.

Cited in 35 Documents

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
76D07 Stokes and related (Oseen, etc.) flows
86A05 Hydrology, hydrography, oceanography

Keywords:

matching conditions; error estimates

Software:

FreeFem++
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\textit{C. Bernardi} et al., ESAIM, Math. Model. Numer. Anal. 42, No. 3, 375--410 (2008; Zbl 1138.76044)
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References:

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