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.