Iterative Stokes Solvers in the Harmonic Velte Subspace |
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Authors: | Gisbert Stoyan |
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Affiliation: | (1) H-1117 Budapest, ELTE University Dept. of Numer. Analysis Pázmány Péter sétány 1/D e-mail: stoyan@valerie.inf.elte.hu homepage: http://valerie.inf.elte.hu/∼stoyan, HU |
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Abstract: | We explore the prospects of utilizing the decomposition of the function space (H
1
0)
n
(where n=2,3) into three orthogonal subspaces (as introduced by Velte) for the iterative solution of the Stokes problem. It is shown
that Uzawa and Arrow-Hurwitz iterations – after at most two initial steps – can proceed fully in the third, smallest subspace.
For both methods, we also compute optimal iteration parameters. Here, for two-dimensional problems, the lower estimate of
the inf-sup constant by Horgan and Payne proves useful and provides an inclusion of the spectrum of the Schur complement operator
of the Stokes problem.
We further consider the conjugate gradient method in the third Velte subspace and derive a corresponding convergence estimate.
Computational results show the effectiveness of this approach for discretizations which admit a discrete Velte decomposition.
Received June 11, 1999; revised October 27, 2000 |
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Keywords: | AMS Subject Classifications: 65N06 65N30 65F10 |
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