A posteriori error analysis for a new fully mixed isotropic discretization of the stationary Stokes-Darcy coupled problem (Q2657237)

Summary: In this paper, we develop an a posteriori error analysis for the stationary Stokes-Darcy coupled problem approximated by conforming the finite element method on isotropic meshes in \(\mathbb{R}^d\), \(d\in\{ 2, 3\} \). The approach utilizes a new robust stabilized fully mixed discretization. The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution plus the stabilization terms. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient.