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\(L^{\infty}\)-estimates for approximated optimal control problems. (English) Zbl 1132.49018

Summary: An optimal control problem for a two-dimensional elliptic equation is investigated with pointwise control constraints. This paper is concerned with discretization of the control by piecewise linear functions. The state and the adjoint state are discretized by linear finite elements. Approximation of order \(h\) in the \(L^\infty\)-norm is proved in the main result.

MSC:

49K20 Optimality conditions for problems involving partial differential equations
49M25 Discrete approximations in optimal control
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35B37 PDE in connection with control problems (MSC2000)
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