A comparison of dual lagrange multiplier spaces for mortar finite element discretizations

Domain decomposition techniques provide a powerful tool for the numerical approximation of partial differential equations. We focus on mortar finite element methods on non-matching triangulations. In particular, we discuss and analyze dual Lagrange multiplier spaces for lowest order finite elements. These non standard Lagrange multiplier spaces yield optimal discretization schemes and a locally supported basis for the associated constrained mortar spaces. As a consequence, standard efficient iterative solvers as multigrid methods or domain decomposition techniques can be easily adapted to the nonconforming situation. Here, we introduce new dual Lagrange multiplier spaces. We concentrate on the construction of locally supported and continuous dual basis functions. The optimality of the associated mortar method is shown. Numerical results illustrate the performance of our approach.