Error Estimates for Discontinuous Galerkin Time-Stepping Schemes for Robin Boundary Control Problems Constrained to Parabolic PDEs

We consider fully discrete finite element approximations of a Robin optimal boundary control problem, constrained by linear parabolic PDEs with rough initial data. Conforming finite element methods for spatial discretization combined with discontinuous time-stepping Galerkin schemes are being used for the space-time discretization. Error estimates are proved under weak regularity hypotheses for the state, adjoint and control variables. Computational examples validating our expected rates of convergence are also provided.