Titlebook: Optimal Shape Design for Elliptic Systems; Olivier Pironneau Book 1984 Springer-Verlag New York Inc. 1984 Design.Diskretisation.Elliptisch

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Design Problems Solved by Standard Optimal Control Theory,This approach ought to be well understood before proceeding to the general case where the control is looked at as a geometric element of the system. For further details and examples, the reader is referred to [40].

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Book 1984applications-oriented study of such physical systems; in particular, those which can be described by an elliptic partial differential equation and where the shape is found by the minimum of a single criterion function. There are many problems of this type in high-technology industries. In fact, most

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Design Problems Solved by Standard Optimal Control Theory,], [29])..We give three examples of this type and use these examples as an opportunity to review the techniques of optimal control developed in [40]. This approach ought to be well understood before proceeding to the general case where the control is looked at as a geometric element of the system. F

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Optimality Conditions,ms may be developed to find feasible numerical solutions. Although it is sufficient to know how to derive such conditions on discrete problems only, it is useful to begin with the study of the continuous case since it is simpler and it may give a valuable interpretation to the solution.

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Discretization with Finite Elements,rential equations, the finite element method (FEM) is the obvious one to choose to use when the domains are the unknowns. We see that the FEM yields much simpler gradients than either the finite difference method or the boundary element method; these two methods are presented in Chapter 8. The FEM i

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