Hamburger Beiträge zur Angewandten Mathematik A Priori Error Estimates for a Finite Element Discretization of Parabolic Optimization Problems with Pointwise Constraints in Time on Mean Values of the Gradient of the State

This article is concerned with the discretization of parabolic optimization problems subject to pointwise in time constraints on mean values of the derivative of the state variable. Central component of the analysis are a priori error estimates for the dG(0)-cG(1) discretization of the parabolic partial differential equation (PDE) in the L∞(0, T ;H1 0 (Ω))-norm, together with corresponding estimates in L1(0, T ;H−1(Ω)) for the adjoint PDE. These results are then utilized to show convergence orders for the discrete approximation towards the solution of the parabolic optimization problem.