Numerical analysis of two grad–div stabilization methods for the time-dependent Stokes/Darcy model

Abstract

We aim to present two algorithms for the non-stationary Stokes/Darcy model. The first one is the standard grad–div stabilization scheme. The other one is a modular grad–div based on the standard Backward Euler code which does not crash or slow down for large value grad–div parameters. Both algorithms cannot only improve the efficiency and accuracy of calculation but also can improve mass conservation, while the modular algorithm can be better. We give a complete theoretical analysis of the stability and error estimations of the algorithms. Finally, the theoretical results are verified by numerical experiments and the advantages of adding grad–div stabilization terms are demonstrated.