Duality Estimates and Multigrid Analysis for Saddle Point Problems Arising from Mortar Discretizations

We present an abstract framework for the analysis of multigrid methods for a saddle point problem arising from mortar finite element discretizations. In contrast to other approaches, the iterates do not have to be in the positive definite subspace. Moreover, our approach also covers the case of nonnested Lagrange multiplier spaces. We apply the multigrid method to different mortar settings including dual Lagrange multipliers, linear elasticity, and a rotating geometry. Numerical results in two dimensions and three dimensions demonstrate the flexibility, efficiency, and reliability of our multigrid method.