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

Christine Bernardi (1) , Tomas Chacon-Rebollo (2) , Frédéric Hecht (1) , Zoubida Mghazli (3)

1 LJLL - Laboratoire Jacques-Louis Lions
2 DEDAN - Departamento de Ecuaciones Diferenciales y An´alisis Numerico
3 EIMA - Equipe d'Ingénierie MAthématique [Kenitra]

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.

Domaines: Analyse numérique [math.NA]

Christine Bernardi, Tomas Chacon-Rebollo, Frédéric Hecht, Zoubida Mghazli. Mortar finite element discretization of a model coupling Darcy and Stokes equations. 2007. ⟨hal-00139167⟩