A non-conforming finite volume element method for the two-dimensional Navier-Stokes/Darcy system

We consider the discretization of the stationary Navier-Stokes/Darcy system in a two-dimensional domain by the non-conforming finite volume element method. We use the standard formulation of the Navier-Stokes/Darcy system in the primitive variables and take as approximation space the non-conforming P-1 elements for velocity and piezometric head and piecewise constant elements for the hydrostatic pressure. We prove that the unique solution of the non-conforming finite volume element method converges to the true solution with optimal order for velocity and piezometric head in discrete H-1 norm and for pressure in discrete L-2 norm, respectively. Finally, some numerical experiments are presented to validate our theoretical results.