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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18594 |
| Date | 06 September 2006 |
| Creators | Pester, Cornelia |
| 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, 05-01 |
| Rights | info:eu-repo/semantics/openAccess |
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