Superconvergence properties of optimal control problems

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Author(s) : Christian Meyer , Arnd Rösch

The paper is published : SIAM Journal on Control and Optimization, 43, pp. 970-985

MSC 2000

49K20 Problems involving partial differential equations
65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Abstract :
An optimal control problem for a 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 $h^2$.

Keywords : Linear-quadratic optimal control problems, error estimates, elliptic equations, numerical approximation, control constraints, superconvergence.