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n L-estimate of the finite element error is proved for a Dirichlet and a Neumann boundary value problem on a three-dimensional, prismatic and non-convex domain that is discretized by an anisotropic tetrahedral mesh. To this end, an approximation error estimate for an interpolation operator that is preserving the Dirichlet boundary conditions is given. The challenge for the Neumann problem is the proof of a local interpolation error estimate for functions from a weighted Sobolev space. [ABSTRACT FROM AUTHOR]

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 [InlineMediaObject 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 [InlineMediaObject 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 [InlineMediaObject not available: see fulltext.] the rate of convergence of the combined approximations in [InlineMediaObject not available: see fulltext.] is proved to be of the order [InlineMediaObject not available: see fulltext.] [ABSTRACT FROM AUTHOR]