{'fraction_non_alphanumeric': 0.025191675794085433, 'fraction_numerical': 0.00547645125958379, 'mean_word_length': 5.175675675675675, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Nitsche- and Fourier-finite-element method for the Poisson equation in axisymmetric domains with re-entrant edges

The paper deals with a combination of the Fourier method with the Nitsche-finite-element method (as a mortar method). The approach is applied to the Dirichlet problem of the Poisson equation in threedimensional axisymmetric domains with reentrant edges generating singularities. The approximating Fourier method yields a splitting of the 3D problem into 2D problems on the meridian plane of the given domain. For solving the 2D problems bearing corner singularities, the Nitschefinite-element method with non-matching meshes and mesh grading near reentrant corners is applied. Using the explicit representation of singular functions, the rate of convergence of the Fourier-Nitsche-mortaring is estimated in some H1-like norm as well as in the L2-norm. Finally, some numerical results are presented.