Justification of the projection method for solving axisymmetric problems of diffraction by locally inhomogeneous bodies

The proof of convergence in the appropriate functional spaces, of the approximate solutions to the exact solution, is discussed for an incomplete numerical projection method of Galerkin type, for axisymmetric problems of the excitation of metal bodies surrounded by a layer of plasma. The cases of two different polarizations, and of ideal and impedance boundary conditions on the metal surface, are distinguished.