SUPERCONVERGENCE ANALYSIS OF FINITE ELEMENT METHODS FOR OPTIMAL CONTROL PROBLEMS OF THE STATIONARY B(?)NARD TYPE

In this paper,we consider the finite element approximation of the distributed optimalcontrol problems of the stationary Bénard type under the pointwise control constraint.The states and the co-states are approximated by polynomial functions of lowest-ordermixed finite element space or piecewise linear functions and the control is approximatedby piecewise constant functions.We give the superconvergence analysis for the control;it is proved that the approximation has a second-order rate of convergence.We furthergive the superconvergence analysis for the states and the co-states.Then we derive errorestimates in L~∞-norm and optimal error estimates in L~2-norm.