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

Abstract

We propose and study an iterative substructuring method for an $$h$$ - $$p$$ 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.