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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18608 |
| Date | 11 September 2006 |
| Creators | Heinrich, Bernd, Jung, Beate |
| Publisher | Technische Universität Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text |
| Source | Preprintreihe des Chemnitzer SFB 393, 05-16 |
| Rights | info:eu-repo/semantics/openAccess |
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