Finite-difference discretizations of quadratic control problems governed by ordinary elliptic differential equations |
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| Authors: | Walter Alt Nils Bräutigam |
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| Affiliation: | 1.Institut für Angewandte Mathematik,Friedrich-Schiller-Universit?t Jena,Jena,Germany;2.Institut für Angewandte Mathematik,Friedrich-Alexander-Universit?t Erlangen-Nürnberg,Erlangen,Germany |
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| Abstract: | In this paper, we analyze finite difference discretizations for a class of control constrained elliptic optimal control problems. If the optimal control has a derivative of bounded variation, we show discrete quadratic convergence in terms of the mesh size h of the discrete optimal controls. Furthermore, based on the optimality conditions, we construct a new discrete control for which we derive continuous error estimates of order h 2. |
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| Keywords: | Linear quadratic optimal control problems Elliptic equations Finite difference approximations Error estimates |
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