The Fourier-Nitsche-mortaring for elliptic problems with reentrant edges |
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Authors: | B Heinrich B Jung |
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Affiliation: | 1.Fakult?t für Mathematik,Technische Universit?t Chemnitz,Chemnitz,Germany |
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Abstract: | 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.
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Keywords: | 65N30 65N35 |
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