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A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares; a finite element approximation is used on the first square and a spectral discretization is used on the second. Two kinds of matching conditions on the interface are presented and compared; in both cases, error estimates are proved.doi:10.2307/2008680 fatcat:eaz3f7jpsjftloins3ycgxaycm