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Fictitious domain/mixed finite element approach for a class of optimal shape design problems. (English) Zbl 0831.65072
The authors construct a fictitious domain method applied to shape optimization problems, using a well-known dualization of the Dirichlet boundary condition on the variable part of the boundary. In a remarkable way, they present an approximation by means of mixed finite elements and prove some interesting convergence results.

MSC:
65K10 Numerical optimization and variational techniques
49M15 Newton-type methods
49J20 Existence theories for optimal control problems involving partial differential equations
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