A multigrid method based on the unconstrained product space for mortar finite element discretizations

The mortar finite element method allows the coupling of different discretiz ations across subregion boundaries. In the original mortar approach, the La grange multiplier space enforcing a weak continuity condition at the interf aces is defined as a modified finite element trace space. Here we present a new approach, where the Lagrange multiplier space is replaced by a dual sp ace without losing the optimality of the a priori bounds. We introduce new dual spaces in 2D and 3D. Using the biorthogonality between the nodal basis functions of this Lagrange multiplier space and a finite element trace spa ce, we derive an equivalent symmetric positive definite variational problem defined on the unconstrained product space. The introduction of this formu lation is based on a local elimination process for the Lagrange multiplier. This equivalent approach is the starting point for the efficient iterative solution by a multigrid method. To obtain level independent convergence ra tes for the W-cycle, we have to de ne suitable level dependent bilinear for ms and transfer operators. Numerical results illustrate the performance of our multigrid method in 2D and 3D.