The Fourier-Nitsche-mortaring for elliptic problems with reentrant edges
The Fourier method is combined with the Nitsche-finite-element method (as a mortar method) and applied to the Dirichlet problem of the Poisson equation in three-dimensional axisymmetric domains with reentrant edges generating singularities. The approximating Fourier method yields a splitting of the 3D problem into a set of 2D problems on the meridian plane of the given domain. For solving the 2D problems bearing corner singularities, the Nitsche-finite-element method with non-matching meshes and mesh grading near reentrant corners is applied. Using the explicit representation of some singularity function of non-tensor product type, the rate of convergence of the Fourier-Nitsche-mortaring is estimated in some H(1)-like norm as well as in the L(2)-norm for weak regularity of the solution. Finally, some numerical results are presented.
fourier method poisson equation non-matching meshes edge singularity finite-element method nitsche-mortaring