A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations

We consider multigrid methods for discontinuous Galerkin H(div,Ω)-conforming discretizations of the Stokes and linear elasticity equations. We analyze variable V-cycle and W-cycle multigrid methods with nonnested bilinear forms. We prove that these algorithms are optimal and robust, i.e., their convergence rates are independent of the mesh size and also of the material parameters such as the Poisson ratio. Numerical experiments are conducted that further confirm the theoretical results.