A new unified stabilized mixed finite element method of the Stokes-Darcy coupled problem: Isotropic discretization

Abstract: 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.