Mortar finite element discretization of a model coupling Darcy and Stokes equations

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

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 3, page 375-410
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Bernardi, Christine, et al. "Mortar finite element discretization of a model coupling Darcy and Stokes equations." ESAIM: Mathematical Modelling and Numerical Analysis 42.3 (2008): 375-410. <http://eudml.org/doc/250402>.

@article{Bernardi2008,
abstract = { 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. },
author = {Bernardi, Christine, Rebollo, Tomás Chacón, Hecht, Frédéric, Mghazli, Zoubida},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Mortar method; finite elements; Darcy equations; Stokes equations.; matching conditions; error estimates},
language = {eng},
month = {4},
number = {3},
pages = {375-410},
publisher = {EDP Sciences},
title = {Mortar finite element discretization of a model coupling Darcy and Stokes equations},
url = {http://eudml.org/doc/250402},
volume = {42},
year = {2008},
}

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: Mathematical Modelling and Numerical Analysis
DA - 2008/4//
PB - EDP Sciences
VL - 42
IS - 3
SP - 375
EP - 410
AB - 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.
LA - eng
KW - Mortar method; finite elements; Darcy equations; Stokes equations.; matching conditions; error estimates
UR - http://eudml.org/doc/250402
ER -

References

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