A Mesh - Independence Principle for Quadratic Penalties Applied to Semilinear Elliptic Boundary Control

• Autorzy: Grossmann C. , Winkler M.
• Języki publikacji: EN

Abstrakty

EN

The quadratic loss penalty is a well known technique for optimization and control problems to treat constraints. In the present paper they are applied to handle control bounds in a boundary control problems with semilinear elliptic state equations. Unlike in the case of finite dimensional optimization for infinite dimensional problems the order of convergence could only be roughly estimated, but numerical experiments revealed a clearly better convergence behavior with constants independent of the dimension of the used discretization. The main result in the present paper is the proof of sharp convergence bounds for both, the finite und infinite dimensional problem with a mesh-independence in case of the discretization. Further, to achieve an efficient realization of penalty methods the principle of control reduction is applied, i.e. the control variable is represented by the adjoint state variable by means of some nonlinear function. The resulting optimality system this way depends only on the state and adjoint state. This system is discretized by conforming linear finite elements. Numerical experiments show exactly the theoretically predicted behavior of the studied penalty technique.

Słowa kluczowe

EN

optimal boundary control; mesh-independence principle; weakly nonlinear elliptic equations; penalty methods for control constraints

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Schedae Informaticae
• Rocznik: 2012
• Tom: Vol. 21
• Strony: 9--26
• Opis fizyczny: Bibliogr. 20 poz, rys.

Twórcy

autor

Grossmann C.

• Institut fur Numerische Mathematik, Technische Universität Dresden, 01062 Dresden, Germany

autor

Winkler M.

• Institut fur Mathematik und Bauinformatik, Universität der Bundeswehr München, 81549 Neubiberg, Germany

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