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Interface control domain decomposition (ICDD) methods for the Stokes problem

journal contribution
posted on 11.09.2015 by Marco Discacciati, Paola Gervasio, Alfio Quarteroni
We study the Interface Control Domain Decomposition (ICDD) for the Stokes equation. We reformulate this problem introducing auxiliary control variables that represent either the traces of the fluid velocity or the normal stress across subdomain interfaces. Then, we characterize suitable cost functionals whose minimization permits to recover the solution of the original problem. We analyze the well-posedness of the optimal control problems associated to the different choices of the cost functionals, and we propose a discretization of the problem based on hp finite elements. The effectiveness of the proposed methods is illustrated through several numerical tests.

Funding

The first author acknowledges funding from the European Union Seventh Framework Programme (FP7/2007- 2013) under grant agreement n◦ 294229.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Coupled Systems and Multiscale Dynamics

Volume

1

Issue

3

Pages

372 - 392

Citation

DISCACCIATI, M., GERVASIO, P. and QUARTERONI, A., 2013. Interface control domain decomposition (ICDD) methods for the Stokes problem. Journal of Coupled Systems and Multiscale Dynamics, 1 (3), pp. 372 - 392

Publisher

© American Scientific Publishers

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2013

Notes

Closed access

ISSN

2330-152X

Language

en

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