A stabilized finite volume method for the evolutionary Stokes-Darcy system

In this paper, we propose a stabilized fully discrete finite volume method based on two local Gauss integrals for a non-stationary Stokes-Darcy problem. This stabilized method is free of stabilized parameters and uses the lowest equal-order finite element triples P1-P1-P1 for approximating the velocity, pressure and hydraulic head of the Stokes-Darcy model. Under a modest time step restriction in relation to physical parameters, we give the stability analysis and the error estimates for the stabilized finite volume scheme by means of a relationship between finite volume and finite element approximations with the lower order elements. Finally, a series of numerical experiments are provided to demonstrate the validity of the theoretical results.