  In this paper, we propose two novel Robin-type domain decomposition methods
based on the two-grid techniques for the coupled Stokes-Darcy system. Our
schemes firstly adopt the existing Robin-type domain decomposition algorithm to
obtain the coarse grid approximate solutions. Then two modified domain
decomposition methods are further constructed on the fine grid by utilizing the
framework of two-grid methods to enhance computational efficiency, via
replacing some interface terms by the coarse grid information. The natural idea
of using the two-grid frame to optimize the domain decomposition method
inherits the best features of both methods and can overcome some of the domain
decomposition deficits. The resulting schemes can be implemented easily using
many existing mature solvers or codes in a flexible way, which are much
effective under smaller mesh sizes or some realistic physical parameters.
Moreover, several error estimates are carried out to show the stability and
convergence of the schemes. Finally, three numerical experiments are performed
and compared with the classical two-grid method, which verifies the validation
and efficiency of the proposed algorithms.
