Error studies of the Coupling Darcy-Stokes System with velocity-pressure formulation

Authors:
Fida Chami;Gihane Mansour;Toni Sayah
Affiliations:
Faculté des Sciences II, Département de Mathématiques, Université Libanaise, Fanar-Maten, Liban;Faculté des Sciences, Université Saint-Joseph, Beyrouth, Liban 1107 2050;Faculté des Sciences, Université Saint-Joseph, Beyrouth, Liban 1107 2050
Venue:
Calcolo: a quarterly on numerical analysis and theory of computation
Year:
2012

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Abstract

In this paper we study the Coupling Darcy-Stokes Systems. We establish a coupled variational formulation with the velocity and the pressure. The velocity is approximated with curl conforming finite elements and the pressure with standard continuous elements. We establish optimal a priori and a posteriori error estimates. We conclude our paper with some numerical simulations.