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In this article, we study the time dependent convection–diffusion–reaction equation coupled with the Darcy equation. We propose and analyze two numerical schemes based on finite element methods for the discretization in space and the implicit Euler method for the discretization in time. An optimal a priori error estimate is then derived for each numerical scheme. Finally, we present some numerical experiments that confirm the theoretical accuracy of the discretization. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]