Etude de Problème d'Optimal Design
Proceedings of the 7th IFIP Conference on Optimization Techniques: Modeling and Optimization in the Service of Man, Part 2
Computational Optimization and Applications
Efficient treatment of stationary free boundary problems
Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
On Convergence in Elliptic Shape Optimization
SIAM Journal on Control and Optimization
On Second Order Shape Optimization Methods for Electrical Impedance Tomography
SIAM Journal on Control and Optimization
Tracking Neumann Data for Stationary Free Boundary Problems
SIAM Journal on Control and Optimization
A new method for inverse electromagnetic casting problems based on the topological derivative
Journal of Computational Physics
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The present paper is concerned with the solution of a Bernoulli type free boundary problem by means of shape optimization. Two state functions are introduced, namely one which satisfies the mixed boundary value problem, whereas the second one satisfies the pure Dirichlet problem. The shape problem under consideration is the minimization of the L 2-distance of the gradients of the state functions. We compute the corresponding shape gradient and Hessian. By the investigation of sufficient second order conditions we prove algebraic ill-posedness of the present formulation. Our theoretical findings are supported by numerical experiments.