Multilevel Preconditioner for the Mortar Method

The main topic of this talk is a new multilevel preconditioner for the lowest order Crouzeix-Raviart finite element on nonmatching grids. The preconditioner is based on the use of a recently developed multilevel preconditioner for the mortar method for the P1 conforming finite element as a black box. For the analysis we use the abstract framework of the auxiliary space methods. The resulting preconditioner for the CR finite element has the same convergence property as the original preconditioner for the P1 mortar finite element. We shall also discuss a new approximate mortar condition for the CR finite element which we have been working on recently. As compared to the standard mortar condition, the new condition has the advantage that we do not need to use the subdomain interior degrees of freedom when calculating the mortar projection.