In this paper, a mixed boundary value problem for
the Laplace-Beltrami operator is considered for
spherical domains in $R^3$, i.e. for domains on
the unit sphere. These domains are parametrized
by spherical coordinates (\varphi, \theta),
such that functions on the unit sphere are
considered as functions in these coordinates.
Careful investigation leads to the introduction
of a proper finite element space corresponding to
an isotropic triangulation of the underlying
domain on the unit sphere. Error estimates are
proven for a Clément-type interpolation operator,
where appropriate, weighted norms are used.
The estimates are applied to the deduction of
a reliable and efficient residual error estimator
for the Laplace-Beltrami operator.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18572 |
| Date | 31 August 2006 |
| Creators | Apel, Thomas, 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 |
| Rights | info:eu-repo/semantics/openAccess |
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