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Description:
This paper is devoted to the construction of a discretization of Poincar'e-Steklov (PS) operators for elliptic boundary value problems with the boundary element method (BEM). PS operators are natural mathematical tools for the investigation of boundary value problems and their numerical solution with domain decomposition (DD) methods based on the finite element (FE) solution of the subproblems (cf. [1], [9]). We will show that the discretizations of PS operators with a direct Galerkin BEM possess the same properties as the FE discretizations if the boundary elements satisfy some natural conditions. Hence the given construction provides a base for the analysis of different DD methods using the BE solution of subproblems, of the coupling of FE and BE methods and related problems.