Higher order dual Lagrange multiplier spaces for mortar finite element discretizations

Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements. In particular, we focus on dual Lagrange multiplier spaces. These non-standard Lagrange multiplier spaces yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces. As a result, standard efficient iterative solvers as multigrid methods can be easily adapted to the nonconforming situation. We construct locally supported and continuous dual basis functions for quadratic finite elements starting from the discontinuous quadratic dual basis functions for the Lagrange multiplier space. In particular, we compare different dual Lagrange multiplier spaces and piece-wise linear and quadratic finite elements. The optimality of the associated mortar method is shown. Numerical results illustrate the performance of our approach.