Author(s) :
Arnd Rösch
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 18-2003
MSC 2000
- 49N10 Linear-quadratic problems
-
65K10 Optimization and variational techniques
Abstract :
An optimal control problem for the 1-d heat equation is investigated
with pointwise control constraints. This paper is concerned with the
discretization of the control by piecewise linear functions.
The connection between the solutions of the discretized problems
and the continuous one is investigated.
Under an additional assumption on the adjoint state an
approximation order $\sigma^{3/2}$ is proved for uniform discretizations.
In the general case it is shown
that a non-uniform control discretization ensure an
approximation of order $\sigma^{3/2}$.
Numerical tests confirm the theoretical part.
Keywords :
Linear-quadratic optimal control problems, error estimates, heat equation, non-uniform grids, numerical approximation, control constraints.