Prince Chidyagwai, A Multilevel Decoupling Method for the NavierStokes/Darcy Model. 
This paper considers a multilevel decoupling method for the coupled NavierStokes/Darcy model describing
a free flowing fluid over a porous medium. The method utilizes a sequence of meshes on which a low
dimensional fully coupled nonlinear problem is solved only on a very coarse initial mesh. On subsequent
finer meshes, the approximate solution in each flow region is obtained by solving a linear decoupled problem
and performing a correction step. The correction step in each domain is achieved by solving a linear
system that differs from the original decoupled system only in the right hand side. We prove optimal error
estimates and demonstrate that for a sequence of meshes with spacing h_j = h^2_{j_1} , the decoupling method is
computationally efficient and achieves the same order of approximation as the fully coupled method.


