Multigrid methods for stabilized nonconforming finite elements for incompressible flow involving the deformation tensor formulation

Abstract — Edge-oriented stabilization methods in the framework of discontinuous Galerkin ap-proaches have been recently proposed by Brenner [3] and particularly by Hansbo and Larson [5] for nonconforming finite element discretizations to satisfy a discrete Korn’s inequality. We develop and analyse corresponding multigrid components in combination with local Pressure-Schur-Complement methods and give numerical examples for incompressible newtonian and non-newtonian fluids