A second-order fractional time-stepping method for a coupled Stokes/Darcy system

Abstract In this paper, a second-order fractional time-stepping method for a Stokes/Darcy system is developed and analyzed. The main feature of this fractional time-stepping method is that we only solve one vector-valued elliptic equation and one scalar-valued Poisson equation for the velocity and pressure of the Stokes equations per time step. Moreover, its central advantage is a time-dependent version of domain decomposition, which has second-order accuracy without requiring an incompressibility constraint for the Stokes equations. The stability of the presented method is established, and numerical experiments are also presented to show its performance.