Analysis of substructuring preconditioners for mortar methods in an abstract framework

A class of preconditioners for the linear system arising from the discretization by the mortar method is studied. We focus on the substructuring approach already applied by Achdou et al. [Y. Achdou, Y. Maday, O. Widlund, Substructuring preconditioners for the mortar method in dimension two, SIAM J. Numer. Anal. 36 (1999) 551-580] to the mortar method for the case of order one finite elements. The estimate that we provide relies on abstract assumptions so our result holds for finite elements of any order, as well as for spaces of different kinds, e.g. wavelets.