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STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM

Nandakumaran, AK and Prakash, Ravi and Raymond, JP (2014) STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM. In: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 35 (3). pp. 323-355.

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Official URL: http://dx.doi.org/10.1080/01630563.2013.812657

Abstract

Homogenization and error analysis of an optimal interior control problem in the framework of Stokes' system, on a domain with rapidly oscillating boundary, are the subject matters of this article. We consider a three dimensional domain constituted of a parallelepiped with a large number of rectangular cylinders at the top of it. An interior control is applied in a proper subdomain of the parallelepiped, away from the oscillating volume. We consider two types of functionals, namely a functional involving the L-2-norm of the state variable and another one involving its H-1-norm. The asymptotic analysis of optimality systems for both cases, when the cross sectional area of the rectangular cylinders tends to zero, is done here. Our major contribution is to derive error estimates for the state, the co-state and the associated pressures, in appropriate functional spaces.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to the TAYLOR & FRANCIS INC, USA
Keywords: Adjoint system; Error estimates; Homogenization; Interior control; Optimal control; Oscillating boundary; Stokes' system
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 10 Mar 2014 07:12
Last Modified: 13 Mar 2014 06:30
URI: http://eprints.iisc.ac.in/id/eprint/48541

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