Finite Element Method and Its Error Estimates for the Time Optimal Controls of Heat Equation

Abstract

In this paper, we discuss the time optimal control problems governed by heat equation. The variational discretization concept is introduced for the approximation of the control, and the semi-discrete finite element method is applied for the controlled heat equation. We prove optimal a priori error estimate for the optimal time $T$, and quasi-optimal estimates for the optimal control $u$, the related state $y$ and adjoint state $p$.