Pearson, John W
(2015)
*
On the development of parameter-robust preconditioners and commutator arguments for solving Stokes control problems.
*
Electronic Transactions on Numerical Analysis,
44
.
pp. 53-72.
ISSN 1068-9613.
(The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)
(KAR id:48158)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. | |

Official URL: http://www.emis.ams.org/journals/ETNA/vol.44.2015/... |

## Abstract

The development of preconditioners for PDE-constrained optimization problems is a field of numerical

analysis which has recently generated much interest. One class of problems which has been investigated in particular

is that of Stokes control problems, that is, the problem of minimizing a functional with the Stokes (or Navier-Stokes)

equations as constraints. In this manuscript, we present an approach for preconditioning Stokes control problems

using preconditioners for the Poisson control problem and, crucially, the application of a commutator argument. This

methodology leads to two block diagonal preconditioners for the problem, one of which was previously derived by

W. Zulehner in 2011 [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 536-560] using a nonstandard norm argument for

this saddle point problem, and the other of which we believe to be new. We also derive two related block triangular

preconditioners using the same methodology and present numerical results to demonstrate the performance of the four

preconditioners in practice.

Item Type: | Article |
---|---|

Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations |

Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | John Pearson |

Date Deposited: | 30 Apr 2015 16:50 UTC |

Last Modified: | 17 Aug 2022 10:58 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/48158 (The current URI for this page, for reference purposes) |

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