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Shape optimization by means of the penalty method with extrapolation. (English) Zbl 0826.65056

Model state problems described by a Poisson equation in a bounded two- dimensional domain with homogeneous Dirichlet boundary condition are considered. The optimal shape design problem is defined by two frequently used cost functionals.
Error estimates are derived. It is shown that the rate of convergence of the penalty method can be increased by means of an extrapolation. The existence of a solution to the approximate optimization problem is discussed and a convergence theorem is proved.
Reviewer: R.Tracht (Essen)

MSC:

65K10 Numerical optimization and variational techniques
49M30 Other numerical methods in calculus of variations (MSC2010)
49J20 Existence theories for optimal control problems involving partial differential equations
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References:

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