Finite Element Nonlinear Galerkin Coupling Method for the Exterior Steady Navier-Stokes Problem (Journal of Computational Mathematics, 2021)
In this paper we represent a new numerical method for solving the steady Navier-Stokes equations in three dimensional unbounded domain. The method consists in coupling the boundary integral and the finite element nonlinear Galerkin methods. An artificial smooth boundary is introduced separating an interior inhomogeneous region from an exterior one. The Navier-Stokes equations in the exterior 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 resulting variational problem. Finally, the existence and error estimates are derived.
Keywords: Navier-Stokes equations; Oseen equations; Boundary integral; Finite element; Nonlinear Galerkin method.