A Mesh-Independence Principle for Quadratic Penalties Applied to Semilinear Elliptic Boundary Control
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RIS BIB ENDNOTEA Mesh-Independence Principle for Quadratic Penalties Applied to Semilinear Elliptic Boundary Control
Publication date: 20.12.2012
Schedae Informaticae, 2012, Volume 21, pp. 9 - 26
https://doi.org/10.4467/20838476SI.12.001.0811Authors
A Mesh-Independence Principle for Quadratic Penalties Applied to Semilinear Elliptic Boundary Control
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.
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Information: Schedae Informaticae, 2012, Volume 21, pp. 9 - 26
Article type: Original article
Titles:
A Mesh-Independence Principle for Quadratic Penalties Applied to Semilinear Elliptic Boundary Control
A Mesh-Independence Principle for Quadratic Penalties Applied to Semilinear Elliptic Boundary Control
Dresden University of Technology, Dresden, Saxony, Germany
Universität der Bundeswehr München , Neubiberg,Germany
Published at: 20.12.2012
Article status: Open
Licence: None
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