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Shape optimization and trial methods for free boundary problem. (English) Zbl 0891.65131
From the author’s abstract: We consider different formulations for a free boundary problem and analyze the related numerical methods. In particular, we formulate various shape optimization problems that are weak forms of a free boundary problem and analyze their properties using the tools of ‘shape calculus’. The main result is that it is possible to influence the conditioning of the shape cost functional and to find a formulation which leads to the optimally conditioned shape Hessian at the solution.
Reviewer: Th.Sonar (Hamburg)

MSC:
65Z05 Applications to the sciences
35R35 Free boundary problems for PDEs
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References:
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