Rodolfo Araya, Cristian Cárcamo, Abner Poza, Eduardo Vino:
An adaptive stabilized finite element method for the Stokes-Darcy coupled problem
For the Stokes-Darcy coupled problem, which models a fluid that flows in a free medium into a porous medium, we introduce and analyze an adaptive stabilized nite element method using Lagrange equal order element to approximate the velocity and pressure of the fluid. The interface conditions between both domains are given by mass conservation, the balance of normal forces, and the Beavers-Joseph-Saffman conditions. We prove the well-posedness of the discrete problem and present a convergence analysis with optimal error estimates in natural norms. Next, we introduce and analyze a residual-based a posteriori error estimator for the stabilized scheme. Finally, we present some numerical examples to show the quality of our scheme.