  We consider control constrained optimal control problems governed by
parameterized stationary Maxwell's system with the Gauss's law. The parameters
enter through dielectric, magnetic permeability, and charge density. Moreover,
the parameter set is assumed to be compact. We discretize the electric field by
a finite element method and use variational discretization concept to
discretize the control. We create a reduced basis method for the optimal
control problem and establish uniform convergence of the reduced order
solutions to that of the original high dimensional problem provided that the
snapshot parameter sample is dense in the parameter set, with an appropriate
parameter separability rule. Finally, we establish the absolute a posteriori
error estimator for the reduced order solutions and the corresponding cost
functions in terms of the state and adjoint residuals.
