Title: Variational discretization of a control-constrained parabolic bang-bang optimal control problem,
Abstract: We consider a control-constrained parabolic optimal control problem without
Tikhonov term in the tracking functional. For the numerical treatment, we use
variational discretization of its Tikhonov regularization: For the state and
the adjoint equation, we apply Petrov-Galerkin schemes from [Daniels et al
2015] in time and usual conforming finite elements in space. We prove a-priori
estimates for the error between the discretized regularized problem and the
limit problem. Since these estimates are not robust if the regularization
parameter tends to zero, we establish robust estimates, which --- depending on
the problem's regularity --- enhance the previous ones. In the special case of
bang-bang solutions, these estimates are further improved. A numerical example
confirms our analytical findings.