Abstract
Domain optimization problems for the two-dimensional stationary flow of incompressible linear-viscous fluids, i.e. the Navier-Stokes equations, are studied. An embedding domain technique which provides an equivalent formulation of the problem on a fixed domain is introduced. Existence of a solution to the domain optimization problem and Fréchet differentiability with respect to the variation of the domain of tracking type cost functionals for the velocity field are proved. A simply computable formula for the derivative of the cost functional is presented. Numerical examples show the advantages of the embedding domain method and the reliability of the derivative formula.
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© 1999 Springer Basel AG
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Slawig, T. (1999). Domain Optimization for the Navier-Stokes Equations by an Embedding Domain Method. In: Hoffmann, KH., Leugering, G., Tröltzsch, F., Caesar, S. (eds) Optimal Control of Partial Differential Equations. ISNM International Series of Numerical Mathematics, vol 133. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8691-8_23
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DOI: https://doi.org/10.1007/978-3-0348-8691-8_23
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9731-0
Online ISBN: 978-3-0348-8691-8
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