A new cement to glue nonconforming grids with Robin interface conditions: The finite element case

Abstract

We present and analyze a new nonconforming domain decomposition method based on a Schwarz method with Robin transmission conditions. We prove that the method is well posed and convergent. Our error analysis is valid in two dimensions for piecewise polynomials of low and high order and also in three dimensions for P1 elements. We further present an efficient algorithm in two dimensions to perform the required projections between arbitrary grids. We finally illustrate the new method with numerical results.