The Second-Order Shape Derivative of Kohn–Vogelius-Type Cost Functional Using the Boundary Differentiation Approach

Jerico B. Bacani and Gunther Peichl
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Jerico B. Bacani: Department of Mathematics and Computer Science, College of Science, University of the Philippines Baguio, Governor Pack Road, Baguio 2600, Philippines
Gunther Peichl: Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, A-8010 Graz, Austria

Mathematics, 2014, vol. 2, issue 4, 1-22

Abstract: A shape optimization method is used to study the exterior Bernoulli free boundaryproblem. We minimize the Kohn–Vogelius-type cost functional over a class of admissibledomains subject to two boundary value problems. The first-order shape derivative of the costfunctional is recalled and its second-order shape derivative for general domains is computedvia the boundary differentiation scheme. Additionally, the second-order shape derivative ofJ at the solution of the Bernoulli problem is computed using Tiihonen’s approach.

Keywords: Bernoulli problem; boundary value problems; shape derivative; boundary differentiation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2014
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