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 of the Poisson equation in three-dimensional axisymmetric domains $\widehat\Omega$ with non-axisymmetric data. The approximating Fourier method yields a splitting of the 3D-problem into 2D-problems. For solving the 2D-problems on the meridian plane $\Omega_a$, 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 some $H^1$-like norm is proved to be of the type ${\mathcal O}(h+N^{-1})$ ($h$: mesh size on $\Omega_a$, $N$: length of the Fourier sum) in case of a regular solution of the boundary value problem. Finally, some numerical results are presented