Decoupled characteristic stabilized finite element method for time-dependent Navier-Stokes/Darcy model

In this article, we propose and analyze a new decoupled characteristic stabilized finite element method for the time-dependent Navier-Stokes/Darcy model. The key idea lies in combining the characteristic method with the stabilized finite element method to solve the decoupled model by using the lowest-order conforming finite element space. In this method, the original model is divided into two parts: one is the nonstationary Navier-Stokes equation, and the other one is the Darcy equation. To deal with the difficulty caused by the trilinear term with nonzero boundary condition, we use the characteristic method. Furthermore, as the lowest-order finite element pair do not satisfy LBB (Ladyzhen-Skaya-Brezzi-Babuska) condition, we adopt the stabilized technique to overcome this flaw. The stability of the numerical method is first proved, and the optimal error estimates are established. Finally, extensive numerical results are provided to justify the theoretical analysis.