Analysis and approximation of optimal control problems for first-order elliptic systems in three dimensions

We examine analytical and numerical aspects of optimal control problems for first-order elliptic systems in three dimensions. The particular setting w e use is that of div-curl systems. After formulating some optimization prob lems, we prove the existence and uniqueness of the optimal solution. We the n demonstrate the existence of Lagrange multipliers and derive an optimalit y system of partial differential equations from which optimal controls and states may be deduced. We then define least-squares finite element approxim ations of the solution of the optimality system and derive optimal estimate s for the error in these approximations. (C) 1999 Elsevier Science Inc. All rights reserved.