In this comparative study, we examine the influence of two different FEM
discretization techniques (conforming $Q_2/P_1$, nonconforming
$/tilde{Q}_1/Q_0$ elements) and solution procedures (various nonlinear
Newton variants and multigrid vs./ Krylov-space solvers for the linear
subproblems) onto the approximation properties and particularly the
total efficiency of corresponding simulation tools for incompressible
fluids. We discuss algorithmic details and give numerical results for
laminar incompressible flow examples including newtonian and
non-newtonian behaviour of {/em Power Law} type.