doi:10.1093/imanum/dri046 Advance Access publication on December 20, 2005 The Fourier-finite-element method with Nitsche mortaring

The paper deals with a combination of the Fourier-finite-element method with the Nitsche-finite-element method (as a mortar method). The approach is applied to the Dirichlet problem for the Poisson equation in 3D axisymmetric domains with non-axisymmetric data. The approximating Fourier method yields a splitting of the 3D problem into 2D problems on the meridian plane of the given domain. For solving these 2D problems, the Nitsche-finite-element method with non-matching meshes is applied. Some important properties of the approximation scheme are derived and the rate of convergence in an H1-like norm as well as in the L2-norm is estimated for a regular solution. Finally, some numerical results are presented