Finite element approach to linear parabolic pointwise control problems of incomplete data

Abstract

In this paper we give a priori error estimates for finite element approximations of linear parabolic problems with pointwise control and incomplete data. We discretise the optimal control problem by using piecewise linear and continuous finite elements for the space discretisation of the state, and we use the backward Euler scheme for time discretisation. We prove a priori error estimates for the state, the adjoint-state as well as for the low-regret pointwise optimal control.