This talk deals with different aspects of edge-oriented/internal penalty stabilisation techniques for nonconforming finite element methods for the numercial solution of incompressible flow problems. There are two separate classes of problems where appropriate stabilization techniques are required: First, the lack of coercivity for nonconforming low order approximations for treating problems with the symmetric deformation tensor instead of the standard gradient formulation in the momentum equation (`Korn`s inequality`) which leads to convergence problems for small Re numbers. Second, for high Re numbers or whenever convective operators are dominant such that the standard Galerkin formulation fails and leads to numerical oscillations, special techniques are needed.
We show that the right choice of edge-oriented stabilization is able to provide excellent results regarding robustness and accuracy for both different cases of applications, and we discuss the sensitivity of the involved parameters w.r.t. mesh distortions and variations of the Re number. Moreover, we explain how efficient multigrid solvers can be constructed to circumvent the arising problems with FEM data structures, and we provide several examples for the numerical efficieny for realistic flow configurations.