Shape optimization for free boundary problems : analysis and numerics

Eppler, Karsten and Harbrecht, Helmut. (2012) Shape optimization for free boundary problems : analysis and numerics. In: Constrained Optimization and Optimal Control for Partial Differential Equations. Basel, pp. 277-288.

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Official URL: http://edoc.unibas.ch/dok/A6002042

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In this paper the solution of a Bernoulli type free boundary problem by means of shape optimization is considered. Four different formulations are com- pared from an analytical and numerical point of view. By analyzing the shape Hessian in case of matching data it is distinguished between well-posed and ill-posed formulations. A nonlinear Ritz-Galerkin method is applied for discretizing the shape optimization problem. In case of well-posedness existence and convergence of the approximate shapes is proven. In combination with a fast boundary element method efficient first and second order shape optimization algorithms are obtained.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Book Section, refereed
Book Section Subtype:Further Contribution in a Book
Publisher:Springer Basel
ISBN:978-3-0348-0133-1 (E-Book) ; 978-3-0348-0132-4 (Print)
Series Name:International Series of Numerical Mathematics
Issue Number:160
Note:Publication type according to Uni Basel Research Database: Book item
Identification Number:
Last Modified:13 Apr 2018 06:17
Deposited On:04 Jan 2013 08:35

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