[en] This paper is concerned with a priori error estimates and convergence analysis of the Fourier-finite-element solutions of the Neumann problem for the Lame equations in axisymmetric domains Ω-circumflex is contained in R³ with reentrant edges. The Fourier-FEM combines the approximating Fourier method with respect to the rotational angle using trigonometric polynomials of degree N (N →∞), with the finite-element method on the plane meridian domain of Ω-circumflex with mesh size h (h → 0) for approximating the Fourier coefficients. The asymptotic behavior of the solution near reentrant edges is described by singular functions in non-tensor product form and treated numerically by means of finite element method on locally graded meshes. For the right-hand side f-circumflex is an element of (L₂(Ω-circumflex))³, it is proved that the rate of convergence of the combined approximations in the norms of (W₂¹(Ω-circumflex))³ is of the order O(h^2-l +N^-(2-l)) (l=0,1). (author)