Substructuring preconditioners for an {$h$}-{$p$} domain decomposition method with interior penalty mortaring

We propose and study an iterative substructuring method for an $$h$$h-$$p$$p Nitsche-type discretization, following the original approach introduced in Bramble et al. Math. Comp. 47(175):103–134, (1986) for conforming methods. We prove quasi-optimality with respect to the mesh size and the polynomial degree for the proposed preconditioner. Numerical experiments assess the performance of the preconditioner and verify the theory