Optimal a priori error estimates of parabolic optimal control problems with a moving point control

摘要

In this paper we consider a parabolic optimal control problem with a Diractype control with moving point source in two space dimensions. We discretizethe problem with piecewise constant functions in time and continuous piecewiselinear finite elements in space. For this discretization we show optimal orderof convergence with respect to the time and the space discretization parametersmodulo some logarithmic terms. Error analysis for the same problem was carriedout in the recent paper [17], however, the analysis there contains a seriousflaw. One of the main goals of this paper is to provide the correct proof. Themain ingredients of our analysis are the global and local error estimates on acurve, that have an independent interest.