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

摘要

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 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 The asymptotic behavior of the solutions of the reduced problems near angular points of Ω a is described by suitable singular functions and treated numerically by linear finite elements on locally graded meshes. For it is proved that the rate of convergence of the combined approximations in is of the order where h and N are the parameters of the finite-element- and Fourier-approximation, respectively, with h→0 and N→∞.