Residual-based a posteriori error estimates for a nonconforming finite element discretization of the Stokes–Darcy coupled problem: isotropic discretization

In this paper we develop an a posteriori error analysis of a nonconforming mixed finite element method for the coupling of fluid flow with porous media flow. The approach utilizes the same nonconforming Crouzeix–Raviart element discretization on the entire domain (Rui and Zhang, Comput Methods Appl Mech Eng 198:2692–2699, 2009). The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.