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SIAM Journal on Control and Optimization

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An Explicit Formula for the Derivative of a Class of Cost Functionals with Respect to Domain Variations in Stokes Flow

SIAM J. Control Optim. Volume 39, Issue 1, pp. 141-158 (2000)

Issue Date: 2000
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Domain optimization problems for the two-dimensional stationary Stokes equations are studied. Fréchet differentiability of a class of cost functionals with respect to the variation of the shape of the computational domain is established. An embedding domain technique provides an equivalent formulation of the problem on a fixed domain and, moreover, a simply computable formula for the derivative of the cost functional with respect to the domain. Existence of a solution to the class of domain optimization problems is proved. Numerical examples show the reliability of the derivative formula.

©2000 Society for Industrial and Applied Mathematics
Permalink: http://dx.doi.org/10.1137/S0363012998347870

KEYWORDS and AMS

Keywords
AMS Subject Classifications
35Q30, 49J50, 65N30, 76D07

PUBLICATION DATA

ISSN:
0363-0129 (print)   1095-7138 (online)
Publisher:
AIP is a member of CrossRef SIAM

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