Optimal Shape Design Subject to Elliptic Variational Inequalities

Authors:
M. Hintermüller;A. Laurain
Affiliations:
hint@math.hu-berlin.de;antoine.laurain@uni-graz.at
Venue:
SIAM Journal on Control and Optimization
Year:
2011

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Abstract

The shape of the free boundary arising from the solution of a variational inequality is controlled by the shape of the domain where the variational inequality is defined. Shape and topological sensitivity analysis is performed for the obstacle problem and for a regularized version of its primal-dual formulation. The shape derivative for the regularized problem can be defined and converges to the solution of a linear problem. These results are applied to an inverse problem and to the electrochemical machining problem.