Finite element method for the Stokes–Darcy problem with a new boundary condition

This paper considers numerical methods for approaching and simulate the Stokes–Darcy problem, with a new boundary condition. We study herein a robust stabilized fully mixed discretization technique, this method ensures the stability of the finite element scheme and does not use any Lagrange multipliers to introduce a stabilization term in the temporal Stokes–Darcy problem discretization. The well-posedness of the finite element scheme and its convergence analysis are also derived. Finally, the efficiency and accuracy of the numerical methods are illustrated by different numerical tests