  We design and analyze a new non-conforming domain decomposition method based
on Schwarz type approaches that allows for the use of Robin interface
conditions on non-conforming grids. The method is proven to be well posed, and
the iterative solver to converge. The error analysis is performed in 2D
piecewise polynomials of low and high order and extended in 3D for $P_1$
elements. Numerical results in 2D illustrate the new method.
