Preconditioners for high order mortar methods based on substructuring

A class of preconditioners for the Mortar Method based on substructuring is studied. We generalize the results of Achdou, Maday and Widlund [1], obtained for the case of order one finite elements, to a wide class of discretization spaces including finite elements of any orders. More precisely, we show that the condition number of the preconditioned matrix grows at most polylogarithmically with the number of degrees of freedom per subdomain.