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

摘要

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. (C) 2019 Elsevier Ltd. All rights reserved.