shape optimal design; finite elements; dual variational formulation; domain optimization; convergence; axisymmetric second order elliptic problem; dual approximate optimal design finite element problem
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. The shape of the domain has to be found so as to minimize a cost functional, which is given in terms of the cogradient of the solution. A new dual finite element method is used for approximate solutions. The existence of an optimal domain is proven and a convergence analysis presented.
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