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Superconvergence properties of optimal control problems. (English) Zbl 1071.49023

Summary: An optimal control problem for a two-dimensional (2-d) elliptic equation is investigated with pointwise control constraints. This paper is concerned with discretization of the control by piecewise constant functions. The state and the adjoint state are discretized by linear finite elements. Approximations of the optimal solution of the continuous optimal control problem will be constructed by a projection of the discrete adjoint state. It is proved that these approximations have convergence order \(h^{2}\).

MSC:

49M25 Discrete approximations in optimal control
49K20 Optimality conditions for problems involving partial differential equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
49N10 Linear-quadratic optimal control problems
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