A New Unified Stabilized Mixed Finite Element Method of the Stokes-Darcy Coupled Problem: Isotropic Discretization

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