The paper deals with a combination of the
Fourier-finite-element method with the
Nitsche-finite-element method (as a mortar method).
The approach is applied to the Dirichlet problem
of the Poisson equation in three-dimensional
axisymmetric domains $\widehat\Omega$ with
non-axisymmetric data. The approximating Fourier
method yields a splitting of the 3D-problem into
2D-problems. For solving the 2D-problems on the
meridian plane $\Omega_a$,
the Nitsche-finite-element method with
non-matching meshes is applied. Some important
properties of the approximation scheme are
derived and the rate of convergence in some
$H^1$-like norm is proved to be of the type
${\mathcal O}(h+N^{-1})$ ($h$: mesh size on
$\Omega_a$, $N$: length of the Fourier sum) in
case of a regular solution of the boundary value
problem. Finally, some numerical results are
presented.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18588 |
| Date | 01 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, 04-11 |
| Rights | info:eu-repo/semantics/openAccess |
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