  Stationary and instationary Stokes and Navier-Stokes flows are considered on
two-dimensional manifolds, i.e., on curved surfaces in three dimensions. The
higher-order surface FEM is used for the approximation of the geometry,
velocities, pressure, and Lagrange multiplier to enforce tangential velocities.
Individual element orders are employed for these various fields. Stream-line
upwind stabilization is employed for flows at high Reynolds numbers.
Applications are presented which extend classical benchmark test cases from
flat domains to general manifolds. Highly accurate solutions are obtained and
higher-order convergence rates are confirmed.
