- AutorIn
- Cornelia Pester
- Titel
- A residual a posteriori error estimator for the eigenvalue problem for the Laplace-Beltrami operator
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:swb:ch1-200601556
- Quellenangabe
- Preprintreihe des Chemnitzer SFB 393, 05-01
- ISSN
- 1619-7186
- Abstract (EN)
- The Laplace-Beltrami operator corresponds to the Laplace operator on curved surfaces. In this paper, we consider an eigenvalue problem for the Laplace-Beltrami operator on subdomains of the unit sphere in $\R^3$. We develop a residual a posteriori error estimator for the eigenpairs and derive a reliable estimate for the eigenvalues. A global parametrization of the spherical domains and a carefully chosen finite element discretization allows us to use an approach similar to the one for the two-dimensional case. In order to assure results in the quality of those for plane domains, weighted norms and an adapted Clément-type interpolation operator have to be introduced.
- Andere Ausgabe
- Link: http://www.tu-chemnitz.de/sfb393/preprints.html
- Freie Schlagwörter (EN)
- Clément-type interpolation, spherical domains
- Klassifikation (DDC)
- 510
- Normschlagwörter (GND)
- A-posteriori-Abschätzung, Eigenwertproblem, Laplace-Beltrami-Operator
- Publizierende Institution
- Technische Universität Chemnitz, Chemnitz
- URN Qucosa
- urn:nbn:de:swb:ch1-200601556
- Veröffentlichungsdatum Qucosa
- 06.09.2006
- Dokumenttyp
- Preprint
- Sprache des Dokumentes
- Englisch