  This paper is the second part of a threefold article, aimed at solving
numerically the Poisson problem in three-dimensional prismatic or axisymmetric
domains. In the first part of this series, the Fourier Singular Complement
Method was introduced and analysed, in prismatic domains. In this second part,
the FSCM is studied in axisymmetric domains with conical vertices, whereas, in
the third part, implementation issues, numerical tests and comparisons with
other methods are carried out. The method is based on a Fourier expansion in
the direction parallel to the reentrant edges of the domain, and on an improved
variant of the Singular Complement Method in the 2D section perpendicular to
those edges. Neither refinements near the reentrant edges or vertices of the
domain, nor cut-off functions are required in the computations to achieve an
optimal convergence order in terms of the mesh size and the number of Fourier
modes used.
