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Finite Element Approximation for Optimal Shape Design


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Preliminaries - Green's formula; abstract setting of optimal shape design problem and its approximation; shape optimization of systems governed by unilateral boundary value state problem - scalar case; approximation of the optimal shape design problems by finite elements - scalar case; numerical realization; shape optimization in unilateral boundary value problems with "flux" cost functional; optimal shape design in contact problems - elastic case; shape optimization of elastic/perfectly plastic bodies in contact; on the design of the optimal covering supported by an obstacle; state constrained optimal control problems and their approximations; FE-grid optimization; concluding remarks on references on optimal shape design and related topics. Appendices: algorithms for FEM; on the differentation of stiffness and mass matrices and force vectors; subgradient method for convex linearly constrained optimization; description of the sequential quadratic programming (SQP) algorithm; on the differentiability of a projection on a convex set in Hilbert space.

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