In this talk, mortar element method is investigated for the coupling of incompressible flow and porous media flow which is relevant to a variety of physical processes. It consists of three parts: the steady coupling of Navier-Stokes and Darcy flows; the unsteady coupling of Stokes and Darcy flows; the unsteady coupling of Navier-Stokes and Darcy flows. The existence and the uniqueness of the weak solution are proved by Galerkin method. The interface part of Navier-Stokes' boundary is chosen as the mortar. The convergence is proved and numerical results verify theoretical analysis.
