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- W3105663113 abstract "We consider finite element solutions to quadratic optimization problems,where the state depends on the control via a well-posed linear partialdifferential equation. Exploiting the structure of a suitably reduced optimalitysystem, we prove that the combined error in the state and adjoint state ofthe variational discretization is bounded by the best approximation error inthe underlying discrete spaces. The constant in this bound depends on theinverse square root of the Tikhonov regularization parameter. Furthermore, ifthe operators of control action and observation are compact, this quasi-bestapproximation constant becomes independent of the Tikhonov parameter asthe mesh size tends to 0 and we give quantitative relationships between meshsize and Tikhonov parameter ensuring this independence. We also derivegeneralizations of these results when the control variable is discretized orwhen it is taken from a convex set." @default.
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- W3105663113 date "2020-01-01" @default.
- W3105663113 modified "2023-10-01" @default.
- W3105663113 title "Quasi-best approximation in optimization with PDE constraints" @default.
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- W3105663113 doi "https://doi.org/10.26083/tuprints-00019330" @default.
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