Tracking Dirichlet Data in L 2 is an Ill-Posed Problem

K. Eppler () and H. Harbrecht ()
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K. Eppler: Technische Universität Dresden
H. Harbrecht: Universität Bonn

Journal of Optimization Theory and Applications, 2010, vol. 145, issue 1, No 2, 17-35

Abstract: Abstract A stationary free boundary problem is solved by tracking the Dirichlet data at the free boundary. The shape gradient and Hessian of the tracking functional under consideration are computed. By analyzing the shape Hessian in case of matching Dirichlet data, it is shown that this shape optimization problem is algebraically ill-posed. Numerical experiments are carried out to validate and quantify the results.

Keywords: Free boundary problem; Shape calculus; Shape Hessian; Ill-posedness; Boundary element method (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-009-9630-4

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