Finite element error estimates for 3D exterior incompressible flow with nonzero velocity at infinity

We consider a stationary incompressible Navier–Stokes flow in a 3D exterior domain, with nonzero velocity at infinity. In order to approximate this flow, we use the stabilized P1–P1 finite element method proposed by Rebollo (Numer Math 79:283–319, 1998). Following an approach by Guirguis and Gunzburger (Model Math Anal Numer 21:445–464, 1987), we apply this method to the Navier–Stokes system with Oseen term in a truncated exterior domain, under a pointwise boundary condition on the artificial boundary. This leads to a discrete problem whose solution approximates the exterior flow, as is shown by error estimates.