FINITE ELEMENT NONLINEAR GALERKIN COUPLING METHOD FOR THE EXTERIOR STEADY NAVIER-STOKES PROBLEM

In this paper we represent a new numerical method for solving the steadyNavier-Stokes equations in three dimensional unbounded domain. The methodconsists in coupling the boundary integral and the finite element nonlinear Galerkinmethods. An artificial smooth boundary is intrdouced seperating an interior inhomogeneous region from an exterior one. The Navier-Stokes equations in theexterior region are approximated by the Oseen equations and the approximate solution is represented by an integral equation over the artificial boundary. Moreover,a finite element nonlinear Galerkin method is used to approximate the resultingvariational problem. Finally, the existence and error estimates are derived.