Coupled and Decoupled Stabilized Finite Element Methods for the Stokes–Darcy-Transport Problem

In this paper, we propose and analyze two stabilized finite element schemes for the Stokes–Darcy-transport model. The first stabilized method is a monolithic scheme with the backward-Euler time discretization, and fully coupled by one Stokes subproblem, one Darcy subproblem, and two transport subproblems. The second stabilized method is a non-iterative partitioned scheme which splits the fully coupled transport problem into two decoupled subproblems. The stability of the proposed schemes can be ensured by some strongly consistent interface terms. The numerical experiments are performed to illustrate the theoretical analysis and demonstrate the reliability and applicability of the proposed schemes.