Defect-deferred correction method for the non-stationary coupled Stokes/Darcy model

Abstract

This paper develops the defect-deferred correction method to solve the non-stationary coupled Stokes/Darcy model. This method is a combination of defect correction method and deferred correction method. And it can not only achieve the second order accuracy in time, but also be applied to the problem with small viscosity and hydraulic conductivity coefficients. The theoretical proof of the stability and the second order accuracy in time are shown. Some numerical experiments are given to verify the error convergence order in time. In addition, compared with the standard Galerkin finite element method, the advantages of the presented method in calculating small viscosity and hydraulic conductivity coefficients will also be reflected in the numerical experiments.