Error estimates for the Fourier-finite-element approximation of the Lamé system in nonsmooth axisymmetric domains

This paper is concerned with the effective implementation of the Fourier-finite-element method, which combines the approximating Fourier and the finite-element methods, for treating the Dirichlet problem for the Lamé equations in axisymmetric domains [inline-graphic not available: see fulltext] with conical vertices and reentrant edges. The partial Fourier decomposition reduces the three-dimensional boundary value problem to an infinite sequence of decoupled two-dimensional boundary value problems on the plane meridian domain [inline-graphic not available: see fulltext] The asymptotic behavior of the solutions of the reduced problems near angular points of Ωa is described by suitable singular functions and treated numerically by linear finite elements on locally graded meshes. For [inline-graphic not available: see fulltext] it is proved that the rate of convergence of the combined approximations in [inline-graphic not available: see fulltext] is of the order [inline-graphic not available: see fulltext] where h and N are the parameters of the finite-element- and Fourier-approximation, respectively, with h→0 and N→∞.