In this paper, finite element discretizations of the
degenerated operator
-ω<sup>2</sup>(y) u<sub>xx</sub>-ω<sup>2</sup>(x)u<sub>yy</sub>=g
in the unit square are investigated, where the
weight function satisfies ω(ξ)=ξ<sup>α</sup>
with α ≥ 0.
We propose two multi-level methods in order to
solve the resulting system of linear algebraic
equations. The first method is a multi-grid
algorithm with line-smoother.
A proof of the smoothing property is given.
The second method is a BPX-like preconditioner
which we call MTS-BPX preconditioner.
We show that the upper eigenvalue bound of the
MTS-BPX preconditioned system matrix grows
proportionally to the level number.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18501 |
| Date | 11 April 2006 |
| Creators | Beuchler, Sven |
| 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, 03-04 |
| Rights | info:eu-repo/semantics/openAccess |
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