The Fourier Finite-element Approximation of the Lamé Equations in Axisymmetric Domains with Edges

This paper is concerned with a priori error estimates and convergence analysis of the Fourier-finite-element solutions of the Neumann problem for the Lamé equations in axisymmetric domains [inline-graphic not available: see fulltext] 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 [inline-graphic not available: see fulltext] with mesh size h (h→0) for approximating the Fourier coefficients. The asymptotic behavior of the solution near reentrant edges is described by singularity functions in non-tensor product form and treated numerically by means of finite element method on locally graded meshes. For [inline-graphic not available: see fulltext] the rate of convergence of the combined approximations in [inline-graphic not available: see fulltext] is proved to be of the order [inline-graphic not available: see fulltext]