A New Error Analysis for Finite Element Methods for Elliptic Neumann Boundary Control Problems with Pointwise Control Constraints

We present a new error analysis for finite element methods for a linear-quadratic elliptic optimal control problem with Neumann boundary control and pointwise control constraints. It can be applied to standard finite element methods when the coefficient s in the elliptic operator are smooth and also to multiscale finite element methods when the coefficients are rough.