The Fourier singular complement method for the Poisson problem. II: Axisymmetric domains (Q818796)

[For part I see ibid. 101, No. 3, 423--450 (2005; Zbl 1084.65123).] The rough structure of this paper, as well as of the companion previous one devoted to prismatic domains, is as follows: i) Poisson problems in axisymmetric and prismatic domains respectively, ii) Fourier expansions, iii) regular-singular decompositions in 2D domain \(\Omega\): theoretical study, iv) discrete formulation: the 2D SCM algorithm singular complement method and v) FSCM- Fourier singular complement method. In both papers, the authors carry out a detailed and sophisticated analysis of generalized SCM as a method to solve 3D singular Poisson problems. The axisymmetric case analysed therein involves only some technical difficulties as compared with the prismatic one. The main result closely parallels that for prismatic domain and states that the rate of FSCM convergence is bounded by a constant depending on the right hand side term of the problem, multiplied by the sum of 2D mesh size and the inverse of the number of Fourier modes used.