ABSTRACT
In this note we describe a new adaptive finite element method for optimal control problems governed by elliptic partial differential equations. The control prob lem is treated by the classical Lagrange formalism yielding the Euler-Lagrange equations as first-order optimality conditions. This indefinite system of partial differential equations for the state variable u ) the Lagrange multiplier A and the control variable q is discretized by a standard finite element method. In this approach the set of admissible solutions is also discretized and we generally obtain inadmissible states. Since discretization in partial differential equations is expensive, at least for praxis-relevant models, the question of how this “model reduction” affects the quality of the optimization result is crucial for an eco nomical computation. The need for adaptive error control is therefore evident.
