A sensitivity study of the artificial viscosity in defect deferred correction method for the coupled Stokes/Darcy model

Abstract

This paper analyzes the sensitivity of the artificial viscosity in the defect deferred correction method for the non-stationary coupled Stokes/Darcy model. For the defect step and the deferred correction step of the defect deferred correction method, we respectively give the corresponding sensitivity systems related to the change of artificial viscosity. Finite element schemes are devised for computing solutions to the sensitivity systems. Finally, we will verify the theoretical analysis results through numerical experiments. Our results reveal that the solution is sensitive for small values of the artificial viscosity, and when the viscosity/hydraulic conductivity coefficients are small.