Coupling boundary integral and finite element methods for the Oseen coupled problem

In this paper, we represent an Oseen coupled problem and related numerical method for solving the nonstationary Navier-Stokes problem in an unbounded domain. The Oseen coupled problem consists of a coupling between the Navier-Stokes problem in an inner region and Oseen problem in an outer region. The related numerical method consists of coupling the boundary integral and the finite element method to solve the coupled problem. The variational formulation of the coupled problem and its well posedness are obtained. The optimal error estimates between the numerical solution of the Oseen coupled problem and the exact solution of the Navier-Stokes problem are provided.