Finite Element Approximation of Wild Optimal Shapes
Denise Chenais, Enrique Zuazua · 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2004
We consider a problem of optimal design in which the functional to minimize depends on the shape of the unknown domain through the solution of a Laplace-Dirichlet equation which is posed on this domain. We are interested in optimal controls whose topology and regularity are not known a priori. In the continuous case, in dimension n = 2, ˘ak [?] proved that there exists an optimal domain in the class of all open subsets of a given bounded open set which have a uniformly bounded number of holes. Here, we consider a finite-element discrete version of this problem and prove that sequences of discrete optimal domains converge in the complementary