A V-cycle multigrid approach for mortar finite elements

Mortar methods, based on dual Lagrange multipliers, provide a flexible tool for the numerical approximation of partial differential equations. The associated finite element spaces are, in general, nonconforming and nonnested. Optimal multigrid results have previously been established for W-cycle and the variable V-cycle multigrid methods. In this paper, we introduce a new multigrid method based on a nested sequence of modified mortar spaces for which we can establish that the V-cycle with one smoothing step has contraction numbers uniformly bounded away from one. To obtain nested mortar spaces, we apply a product form of certain corrections at the interfaces. Numerical results demonstrate the efficiency of the resulting multigrid solver.