Volume 42, Number 3, May-June 2008
|Page(s)||375 - 410|
|Published online||03 April 2008|
Mortar finite element discretization of a model coupling Darcy and Stokes equations
Laboratoire Jacques-Louis Lions, C.N.R.S.
& Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu,
75252 Paris Cedex 05, France. email@example.com; firstname.lastname@example.org
2 Departamento de Ecuaciones Diferenciales y Análisis Numerico, Universidad de Sevilla, Tarfia s/n, 41012 Sevilla, Spain. email@example.com
3 Équipe d'Ingénierie Mathématique, LIRNE, Faculté des Sciences, Université Ibn Tofail, B.P. 133, Kénitra, Morocco. firstname.lastname@example.org
Revised: 3 October 2007
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.
Mathematics Subject Classification: 65N30 / 65N55 / 76M10
Key words: Mortar method / finite elements / Darcy equations / Stokes equations.
© EDP Sciences, SMAI, 2008
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