Nitsche- and Fourier-finite-element method for the Poisson equation in axisymmetric domains with re-entrant edges

• Main Authors: Heinrich, Bernd, Jung, Beate
• Language: English
• Published: Technische Universität Chemnitz 2006
• Subjects: info:eu-repo/classification/ddc/510; ddc:510; Eckensingularität; Finite-Elemente-Methode; Poisson-Gleichung; Fourier method; Nitsche-mortaring; non-matching meshes
• Online Access: http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601691; https://monarch.qucosa.de/id/qucosa%3A18608; https://monarch.qucosa.de/api/qucosa%3A18608/attachment/ATT-0/; https://monarch.qucosa.de/api/qucosa%3A18608/attachment/ATT-2/; https://monarch.qucosa.de/api/qucosa%3A18608/attachment/ATT-3/; https://monarch.qucosa.de/api/qucosa%3A18608/attachment/ATT-4/; https://monarch.qucosa.de/api/qucosa%3A18608/attachment/ATT-5/; https://monarch.qucosa.de/api/qucosa%3A18608/attachment/ATT-6/; https://monarch.qucosa.de/api/qucosa%3A18608/attachment/ATT-7/; https://monarch.qucosa.de/api/qucosa%3A18608/attachment/ATT-8/

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 Nitsche finite-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 $H^1$-like norm as well as in the $L_2$-norm. Finally, some numerical results are presented.