A POSTERIORI ERROR ESTIMATE FOR BOUNDARY CONTROL PROBLEMS GOVERNED BY THE PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

In this paper,we discuss the a posteriori error estimate of the finite element approximationfor the boundary control problems governed by the parabolic partial differentialequations.Three different a posteriori error estimators are provided for the parabolicboundary control problems with the observations of the distributed state,the boundarystate and the final state.It is proven that these estimators are reliable bounds of the finiteelement approximation errors,which can be used as the indicators of the mesh refinementin adaptive finite element methods.