  In this paper we develop an a priori error analysis of a new unified mixed
finite element method for the coupling of fluid flow with porous media flow in
$\mathbb{R}^N$, $N\in\{2,3\}$ on isotropic meshes. Flows are governed by the
Stokes and Darcy equations, respectively, and the corresponding transmission
conditions are given by mass conservation, balance of normal forces, and the
Beavers-Joseph-Saffman law. The approach utilizes a modification of the Darcy
problem which allows us to apply a variant nonconforming Crouzeix-Raviart
finite element to the whole coupled Stokes-Darcy problem. The well-posedness of
the finite element scheme and its convergence analysis are derived. Finally,
the numerical experiments are presented, which confirm the excellent stability
and accuracy of our method.
