Meyer, C.; Rösch, A. \(L^{\infty}\)-estimates for approximated optimal control problems. (English) Zbl 1132.49018 SIAM J. Control Optim. 44, No. 5, 1636-1649 (2006). 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. Cited in 31 Documents 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) Keywords:linear-quadratic optimal control problems; error estimates; elliptic equations; numerical approximation; control constraints PDFBibTeX XMLCite \textit{C. Meyer} and \textit{A. Rösch}, SIAM J. Control Optim. 44, No. 5, 1636--1649 (2006; Zbl 1132.49018) Full Text: DOI