Robust multigrid methods for nearly incompressible elasticity

We consider multigrid methods for problems in linear elasticity which are r obust with respect to the Poisson ratio. Therefore, we consider mixed appro ximations involving the displacement vector and the pressure, where the pre ssure is approximated by discontinuous functions. Then, the pressure can be eliminated by static condensation. The method is based on a saddle point s moother which was introduced for the Stokes problem and which is transferre d to the elasticity system. The performance and the robustness of the multi grid method are demonstrated on several examples with different discretizat ions in 2D and 3D. Furthermore, we compare the multigrid method for the sad dle point formulation and for the condensed positive definite system.