Residual-based a posteriori error estimates for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si3.svg"><mml:mrow><mml:mi>h</mml:mi><mml:mi>p</mml:mi></mml:mrow></mml:math> version of the finite element discretization of the elliptic Robin boundary control problem

Optimal control problems governed by partial differential equations have become a very active and successful research area. So, in this paper, we analyzed priori posteriori error estimates for the hp finite element discretization of elliptic Robin boundary problems. With discrete continuous optimality conditions problem, constructed estimators. Based on residual model coupled state approximations, upper bound is proved using Scott–Zhang-type quasi interpolation estimates. In order to provide optimality, lower shown some polynomial inverse weighted Sobolev spaces. Such estimators can be used construct reliable adaptive methods optimal