  In Gander et al. [2004] we proposed a new non-conforming domain decomposition
paradigm, the New Interface Cement Equilibrated Mortar (NICEM) method, based on
Schwarz type methods that allows for the use of Robin interface conditions on
non-conforming grids. The error analysis was done for P1 finite elements, in 2D
and 3D. In this paper, we provide new numerical analysis results that allow to
extend this error analysis in 2D for piecewise polynomials of higher order and
also prove the convergence of the iterative algorithm in all these cases.
