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

A new Cement to Glue non-conforming Grids with Robin interface conditions: the finite element case