Incompressible finite element methods for Navier-Stokes equations with nonstandard boundary conditions in ${\bf R}\sp 3$

This paper is devoted to the steady state, incompressible Navier-Stokes equations with nonstandard boundary conditions of the form ${\mathbf{u}} \cdot {\mathbf{n}} = 0$, $\mathbf{curl}\;{\mathbf{u}} \times {\mathbf{n}} = {\mathbf{0}}$, either on the entire boundary or mixed with the standard boundary condition ${\mathbf{u}} = {\mathbf{0}}$ on part of the boundary. The problem is expressed in terms of vector potential, vorticity and pressure. The vorticity and vector potential are approximated with curl-conforming finite elements and the pressure with standard continuous finite elements. The error estimates yield nearly optimal results for the purely nonstandard problem.