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On the development of parameter-robust preconditioners and commutator arguments for solving Stokes control problems

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)

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. (Contact us about this Publication)
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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: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: John Pearson
Date Deposited: 30 Apr 2015 16:50 UTC
Last Modified: 29 May 2019 14:28 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/48158 (The current URI for this page, for reference purposes)
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