Nonconforming FEM approaches have proven advantageous behaviour for incompressible flow problems due to their excellent stability properties w.r.t. LBB condition and anisotropic mesh deformation. Moreover, together with discrete projection techniques or Pressure Schur Complement methods they allow very efficient FEM solvers for nonstationary problems. And, finally, their edge-oriented degrees of freedom lead to very compact data structures which have big advantages for parallel high performance computations. So, they are quite natural candidates to include error control mechanisms and concepts for adaptivity w.r.t. meshes in space and time.

However, for formulations including the deformation tensor D(u) which are typical for nonlinear fluids and viscoelastic flow, these approaches are unstable due to not satisfying a discrete Korn`s inequality. Based on the stabilization techniques which have been recently proposed by Hansbo and Larson in a discontinuous Galerkin context, we give a numerical analysis of the resulting stability and accuracy behaviour. Moreover, we explain how efficient multigrid solvers can be constructed and give examples for the numerical efficiency for realistic flow configurations.