A two-grid decoupled penalty finite element method for the stationary Stokes-Darcy problem (Q6591765)

First, the authors provide a weak formulation of the coupled Stokes-Darcy system in 2D and 3D, and then they introduce the penalty formulation of this system along with its associated analytical properties. A finite element method for solving the coupled penalty system is analyzed, and the corresponding error estimates are provided. In the core of the work, a two-grid decoupled penalty finite element method is constructed in order to solve the same system. An error analysis is also done for this formulation. Two numerical experiments are carried out to validate the two-grid decoupled penalty finite element method scheme. The numerical results indicate that the proposed scheme can achieve the same accuracy as the directly coupled finite element method while reducing cost.